Ten minutes before the National are due on stage at Café de la Danse in Paris, the news breaks: Notre Dame is on fire. The inner thoughts of the Grammy-award-winning American alternative rock band are ticker-tape flashes of catastrophe. They were a fledgling band in Brooklyn when 9/11 happened; they are in Paris tonight, four years on from the Bataclan theatre massacre, and two years on from the UK’s Manchester Arena bombing. The band’s frontman Matt Berninger feels certain it is a hate crime and visualises detonating planes and mass shootings. Multi-instrumentalist/songwriter Bryce Dessner moved to Paris in 2015 and is having Bataclan flashbacks. “Are we really gonna play?” he wonders.

Film director Mike Mills, the National’s creative director for this year, is watching the dramatic news images, recalling churches on fire in the second world war and feeling it is the 1930s all over again, illiberal rhetoric everywhere, dismayed that Europe has taken another hit. Bassist Scott Devendorf, meanwhile, had a text before news reached him, from a friend in the United States, saying “Notre Dame on fire”. He thought it was about the Notre Dame baseball team in New Jersey pulverising their opponents.

Half an hour later, the National are playing a new song on stage, Hairpin Turns, a haunting, piano-led lament. “What are we going through? You and me,” implores Berninger, in his mournful baritone. “Every other house on the street’s burning / Days of brutalism and hairpin turns …”

It seems we’ve become a Generation Catastrophe, with everyone over the age of 10 collectively fine-tuned to threat, anxiety, paranoia and impending apocalypse. On the streets of Paris today, Extinction Rebellion protesters hoist flags depicting their egg-timer logo. Since 1999, the National have been the sound of human heartbreak, excavators of emotional ennui (or, the US’s Radiohead via REM, Nick Cave and Joy Division). In the year of their 20th anniversary, as humanity’s existential sadness seems to deepen every day, the National are the perfect band for these times, aren’t they? “The sound of the apocalypse!” hoots Devendorf. “There is something to that. We’re therapists, in these times. Maybe not, we’re not qualified!”

Twenty-four hours earlier, in Paris’s Pin-Up Studios, Mills is directing the video for Hairpin Turns, band members performing solo in minimalist white space. They shouldn’t even be here, due lengthy time off after touring worldwide for 2017’s quietly enormous, global No 1 album Sleep Well Beast had left them “exhausted, batteries drained”, according to Berninger. Instead, they took up a late-2017 email offer of visual collaboration from Mills, the 53-year-old Oscar-nominated director of 2016’s 20th Century Women (and a lifelong National scholar). The result, I Am Easy to Find, is a 24-minute film (one woman’s life in pivotal moments, elegantly played by Oscar-winner Alicia Vikander) and a Mills-edited, orchestrally hypnotic album featuring six female vocalists (inspired by Vikander’s character).

Three will join them on stage for two shows in Paris – the former Bowie bassist Gail Ann Dorsey and the This Is the Kit frontperson Kate Stables, alongside Bryce’s wife, the French songwriter Pauline De Lassus (and a seven-piece male/female string section). For the five-man troupe from Ohio, who have famously struggled with infighting, and now live across the US and Europe, the result, thrills Berninger, is both “creative reboot” and more universal prism for his male neuroses.

In Pin-Up, meanwhile, Berninger, 48, has a new best friend, seven-year-old Hopper, Mills’s long-haired son, who is standing at a monitor yelling, er, encouragement to his new-found bearded buddy. “Matt!” he yelps. “You look really good … cos I can’t see your face!”

“Hey, look at this …” responds a cackling Berninger (himself dad to 10-year-old Isla), letting his microphone stand fold double with a comedy duck-whistle sound effect. It is relaxed, upbeat behaviour you don’t expect from the American Bard of Despair, an adolescent Morrissey/Smiths obsessive who abandoned his well-paid graphics career at 28 for the chaos of musical life.

Meanwhile, multi-instrumentalist /songwriter/producer Aaron Dessner, 43, is explaining he and twin brother Bryce’s intriguing ancestry, a lineage of Scots, Jews and Native Americans. The twins are the National’s musical heart, virtuoso musicians versed in intricate melancholy. Ask Aaron if their propensity for sadness might be in their memory DNA, from persecuted peoples, and Bryce interjects, smiling broadly. “I think, in 2019, as middle-aged white men, we’d have a hard time calling ourselves persecuted in any way. So … no!”

The morning after the Notre Dame fire, the Dessners are seated at breakfast in a fashionable hotel, a shy, eloquent pair. Aaron lives between Copenhagen and upstate New York (home to his timber-framed Long Pond studio), and will soon move to Paris with his wife and three young children to join his twin brother. In the US, on the school run, he has taken to switching off radio news “because I don’t want them hearing about kids in cages and mass shootings”. Bryce, who lives two blocks from Notre Dame, saw symbolism in last night’s dramatic events. “A melting cathedral,” he laments. “When so many institutions are crumbling, basic concepts of liberalism, it’s like everything you think is permanent can be erased.”

Mills’s influence on the National’s permanently melancholy sound, muses Aaron, in no way erased it, more expanded it, with “choral, baroque arrangements,” he says. “And he took a lot of tension out of the band – suddenly there was this higher authority.” Today, Aaron says his connection to musical sadness may be innate after all. “I suffered from depression in high school,” he explains. “It’s clinical. I was a lucky kid, nice family, nobody did anything wrong to me. But from the earliest, writing music with Bryce was therapy. That’s why a lot of our music is meditative, the layers, rhythms, patterns.”

He has studied twin phenomena, how “one twin will manifest [depression]. I do have that streak and I actively fight it.” In 2016, he produced Frightened Rabbit’s Painting of a Panic Attack and saw singer Scott Hutchison lost to suicide in 2018. Chaotic creative lifestyles, he knows, can exacerbate things. “There’s a toll to this life, with no structure or control,” he says – perhaps another reason the twins need to be geographically close. “There’s deep friendships in the band but it could end tomorrow,” he notes. “For Bryce and I, the main reason we make music is to be together.”

On a hotel bed upstairs, Berninger and Mills are sitting side by side, legs outstretched, cackling like teenagers as befits old buddies, despite being strangers until 2017. “It was like getting an email from Bruce Springsteen!” hollers Berninger, an enormous personality, in bewildering contrast to the distraught neurotic he so deftly sketches in song. Mills happily listens while a Berninger barrage ensues, over these “brutal times”, the rise of global fascism, over “an elevated level of violence of language and thought” and his admiration for children, “who are not yet ruined”.

Like the Dessners, art is their personal therapy. “Art is like, what do you think about when you think?” declares Berninger. “About the things you desire, things you’re worried about losing. It’s about complicated mental questions. Put in everything you don’t understand, that you can’t figure out.”

Mills’s I Am Easy to Find film is both a simple concept and cleverly, uniquely conceived, Vikander is convincing (and moving) as she portrays a woman from baby to grandma, with no CGI wizardry involved. Mills’s work often centres on women, something he ascribes to growing up with older sisters (while his dad, after his mother’s death, came out as gay aged 75). “My plight is to not understand women,” he smiles, “but keep trying.” Mills’s creative direction for the I Am Easy to Find album was non-musical, his input “like a fancy cheerleader”, either vetoing tired ideas or shouting “Cool!” in encouragement.

“It felt like a break from the National,” enthuses Berninger, who mostly worked from his home in LA, co-writing lyrics with his wife Carin Besser, Mills cheerleading with Aaron in Long Pond, “which was good for us, good for Mike, not being in the middle of us fighting! Producers are often there to help make hits. We were like, Mike, we’ve never had a hit, clearly we don’t need the hits. So what’s good art?”

Given the perpetual creative struggles, you wonder if he ever thinks about stopping the band. “We think about it all the time,” he announces, alarmingly, before tempering his outburst. “We just need to reboot, a lot.”

As the pair spring from the bed, you wonder what the National will do for the next reboot, when Mills goes back to film-making? “I’ll be sitting,” jokes Berninger, “behind him.”

In another hotel room, alone, Devendorf (brother of National drummer Bryan, who sits out interviews) is pondering what happens when a band is no longer struggling, when struggle so often fuels creative drive. “You can get lazy. I’m familiar with that concept!” He laughs. “People do get soft from living too high on the hog. But music still brings us joy.” Devendorf is a wry character, who openly mocks Berninger’s original lyrical ideas for a new, six-minute autobiographical song, Not in Kansas. “It was 12 minutes,” he scoffs. “Really? You’re fucking welcome! Mike Mills was mentioned, Mike Mills from REM and a massage therapist. What is this laundry list?”

Bryce often thinks about life beyond the National: today he is a prolific composer for global orchestras, recently immersed in the Minimalist Dream House project with Thom Yorke and fellow classical virtuosos. “Many of the greatest rock bands never made it to 10 years,” he notes, now alone at the breakfast table. “Egos, desires, creative ambitions – constantly subsuming that in the greater cause is a challenge! Everybody has had their chapter of really struggling with it. After this there’ll probably be a long break.”

His personal priorities are shifting. Recently, he saw “our family kind of imploding”. He is loathe to elaborate but says “just the relationship with our parents, seeing things you always expected to be there, suddenly not there”. It’s new parenthood, though, that is changing everything, as he was the last of the National to become a father two years ago. Today, between band and brass section, there are 12 children.

“Every time you tour, you’re taking time away from these small people who really value it,” he says. “You don’t get those years back, obviously. So that’s really tricky. When you’re 22, the band is your life, but there are things more important than the band now, there really are.”

He ponders what is left for the National to achieve, the sometime alt-rock underdogs now a worldwide arena band who have headlined London’s O2 Arena and the Royal Albert Hall. “Dreams you’d never expect, especially our band,” he says. “So it becomes, are we gonna go for Everest now?”

What is Everest, now, for them? “Um. I think …” Enormous pause. “I think the band is at a crossroads,” he eventually replies. “The National’s been a fixture for my entire adult life. Some day I won’t have it. Everything about life, now, certainly pulls on the fabric. It may become harder. Allowing each other to realise dreams elsewhere, as artists, as human beings. We don’t foresee ourselves doing Rolling Stones stadium tours. So, Everest? Maybe headlining Central Park. Actually, we headlined Central Park …”

He stops, wary of this suddenly ominous talk. “But a band is a family,” he concludes. “You need to care for your family. That is now our Everest. And it’s something I don’t want to lose.”

Inside the scarlet-hued Olympia theatre, in acute contrast to the earnest, sombre atmospherics throughout I Am Easy to Find, Berninger is laughing, accidentally knocking over his mic stand, shouting, “I’m pissed!” His dynamic stage theatrics are almost comical, the back of one hand pressed dramatically to his brow, new song Where Is Her Head seeing him howl, over and over: “I think I’m hittin’ a wall!”

When they close with beloved non-hit Fake Empire, Paris is finally on its feet in musical recognition. The three female vocalists, string and brass sections, are now gone, the National once again an apocalyptic five-man rock band. Bryce, in the dying notes, thrusts his guitar into the air, creating an iconic, defiant silhouette. Like Notre Dame, the original gothic jewel at the National’s core remains. For now.

I Am Easy to Find is out on 17 May. The National play the British Summer Time festival, Hyde Park, London, on 13 July. Tickets: bst-hydepark.com

• This article was amended on 3 May 2019. The This Is the Kit frontperson is Kate Stables, not Staples, as stated in an earlier version.