Some have compared it to a pile of broken paving stones. Others, to a rusty spaceship crash-landed on the edge of the city. The architect of Paris’s new Philharmonie concert hall, Jean Nouvel, promised that it would be “one of the most remarkable symphonic buildings existing.” Remarkable indeed, for its escalating budgets, endless delays and bitter rows, which climaxed this week when Nouvel boycotted the inauguration of his own building, accusing his client of “contempt for architecture, for the profession and for the architect of the most important French cultural program of the new century.”

Running two years late and three times over its original budget, the €390m concert hall was still surrounded by an army of workmen frantically fixing cladding panels to the facade when the conductor took to his dais on Wednesday evening. But Nouvel was conspicuously absent. “The architecture is martyred, the details sabotaged,” he wrote in a blistering editorial in Le Monde that day, describing the finished result as a kind of architecture “that oscillates between counterfeiting and tampering”.

Looming above the Parc de la Villette in the east of the city like one of George Lucas’s menacing starships, the building certainly seems to embody the anguish it has caused both architect, client and taxpayer. It is a tyrannical hulk of a thing, its gargantuan grey shell wrenched to and fro as if battered by an intergalactic skirmish, sooty scorch marks burnt across its crumpled mass. It rises up in a series of tilted plates, clad with interlocking bird-shaped aluminium tiles, designed to draw visitors up from the park along zigzagging routes to the rooftop, where panoramic views can be had, with space for 700 people to picnic on its elevated plateau. Paris asked for a concert hall and it got a new mountain to boot, the result of an extraordinary tectonic rupture on the ring road.

Entered via an imposing staircase or up a momentous ramp, the foreboding form is framed with the language of inclusion and accessibility. The building’s location, in the comparatively deprived 19th arrondissement, is part of an effort to engage new audiences, seeing the city’s main symphony venue move from the art deco Salle Pleyel in the posh west side of town. The great wing that crowns the Philharmonie’s summit with a jaunty quiff is described by its director Laurent Bayle as “extending a hand to the banlieues.” The concert programme will be projected on to its aluminium skin, an urban billboard intended to lure people from the rundown eastern suburbs to see what lies within the mysterious mothership. They might be surprised to find not cyborgs but men in bow ties.

If it is a bewildering arrival in the city, it finds solace here among a zoo of other architectural misfits. The Parc de la Villette is the work of Bernard Tschumi, French godfather of the punkish deconstructivist style, whose bright red follies dot a landscape punctuated by a plethora of strange experiments from the 80s and 90s. There is a mirrored geodesic dome and a hangar-like science museum, a tensile rubbery performance arena and an undulating conservatoire – and, right next to the Philharmonie, the wild postmodern assemblage of Christian de Portzamparc’s Cité de la Musique, already home to a 1,000-seat concert hall.

It feels like Nouvel has arrived late to the party, his big metal mountain still drunk on the same 90s whimsy as its neighbours. There is more than a whiff of François Mitterrand’s grands projets still hanging in the air, and the light-headed architectural exuberance that his cultural programme sponsored, along with a strange feeling of deja vu. For, although you might not have seen anything quite this weird before, the Philharmonie effectively channels the last two decades of architecture’s more extravagant tendencies into one great lump.

There is the jagged prow borrowed from Daniel Libeskind, the billowing waves from Zaha Hadid, the chiselled zigzagging rooftop walk from Snøhetta, all tied together with the mishmash bricolage lunacy of Coop Himmelblau – whose contorted Confluence Museum just opened in Lyon, bearing a strong family resemblance to the Philharmonie. It is the kind of arms-length statement architecture that has been incubated in the anything-goes climes of China and the Middle East for the past few years; but it is a shock to the system to see it land in a European capital, on quite such a scale. The result is a greatest-hits mash-up of dictators’ icons, a building that blends the excesses of “starchitectural” culture into one over-seasoned potage.

Still, concertgoers say it’s what’s on the inside that counts, and the 2,400-seat auditorium certainly sounds promising from the first night. Reached from the ramping plates that spiral up into the building, it takes the form of an enveloping creamy womb, as soft and seductive as the exterior is angular and aggressive. The acoustics have been praised for their clarity and transparency (thanks to the work of four groups of acoustical engineers), with a warm resonance provided by the vast volume of the space, while retaining a sense of intimacy – you can almost sit close enough to read the percussionist’s score.

The seating blocks are arranged on cascading balconies around the stage, in the vineyard model established by Hans Scharoun’s seminal 1963 Berlin Philharmonic, but they are suspended within a much bigger shell, which prolongs the reverberation time and gives the visual impression, thanks to clever lighting tricks, that the audience is hovering in an endless void. The seats are sumptuous – this is first-class space travel – and the room can be reconfigured to accommodate 3,000 for world music and rock concerts.

Within the twisted bowels of the building there is also a decent-sized exhibition space, two restaurants, six rehearsal rooms and substantial education studios, though some of these spaces feel like a bit of an afterthought, tucked into the awkward folds of the grand gesture. The interiors aren’t completely finished, so it’s hard to judge, but the material finishes seem to be the usual Nouvel palette of brooding boudoir, with hints of S&M in places – including sheets of nails plunging from the ceiling.

The architect himself remains adamant that the Philharmonie has “shot itself in both feet” by tampering with his plans and opening too soon, and the compromise is certainly wrought in its details. But, just like its oddball neighbours, it will no doubt win the city’s affections with time, as another bizarre addition to this whimsical cultural theme park, a late-born monument from a bygone era.

• This article was amended on 21 January 2015 to clarify that the workmen were frantic, not fanatic.