In 2010, Héloïse Letissier arrived in London searching for an identity and seeking adventure. Six years later, she’s back with a new guise, playing to a sold-out crowd for her first headline gig in the capital. “This is where it all started for me,” she says, her mile-wide smile one of pride and disbelief. “A freaky idea, to let a stage character live my thoughts.”

That alter-ego is Christine – “I believe I am a little boy dreaming of being Beyoncé,” Letissier explains – and the Queens, her imaginary band named after three London drag queens encountered on that fateful trip. It’s a construct that’s made the 27-year-old ex-theatre student a superstar back home in France, with two Victoires de la Musique awards, the French equivalent of the Grammies, to her name and the dubious honour of having been spanked by Madonna at the latter’s recent Paris show. In February, Christine and the Queens released an English version of their 2014 debut album Chaleur Humaine and Letissier describes this show not as a homecoming, but a “first date”. And, like an ardent suitor, she goes all out to impress.

A tiny figure dressed in black and dwarfed by four male dancers, Letissier is a fevered force of nature on stage, a place she describes as a “free zone”. Under suspended, off-balance strip lights, she leaps with balletic grace and wrestles with herself like a wilful child, her hands graceful then violent as she performs a series of jagged, Michael Jackson-inspired, hip-thrusting, chin-jutting dance routines with a look of fierce determination. CATQ’s blend of hip-hop, chamber and electropop give this boundless energy an engaging versatility. Paradis Perdus, a mash-up of French singer Christophe’s 1972 chanson and Kanye West’s 2008 hit Heartless, is sung with crystal-clear sincerity and absolute authenticity. A huge screen behind Letissier enables filmed contributions from Tunji Ige, who raps over haunting ballad No Harm Is Done, and Perfume Genius, who pops up for torch song Jonathan, while her guitarist and two keyboardists add shivery chords, undulating rhythms and club beats to Science Fiction and Safe and Holy.

Letissier codifies the contrasting, potent moods of her music with her unabashed faith in the transformative power of pop. She relishes a cover of Pump Up the Jam and a sample of Chaka Khan’s I Feel For You, and is in her element listening to the crowd singing CATQ favourites Tilted and Saint Claude, before they serenade her, a capella, on the magnificent Nuit 17 à 52. And while she describes herself as “a flower, fighting the wind,” Letissier leaves London having blossomed into an unquestionable star.

• At the Roundhouse, London, 3 May. Box office: 0300-678 9222.