A Camille concert is an extraordinary experience. Over two hours, the maverick singer writhes barefoot on the floor, dances like a galloping horse, howls like a wolf, sings audacious harmonies with a trio of backing vocalists and hits the kind of high notes that might only be audible to dogs. She sings in English about adultery and ecology; she sings in French about the futility of planting a Twix or a Mars bar in the soil, or how pregnancy turns a man’s semen into milk. She starts her set with a mournful, melismatic reading of Joni Mitchell’s Blue and reaches a truly bestial climax with a gospel punk version of the Dead Kennedys’ Too Drunk to Fuck.

In an Anglo-American pop world that has traditionally treated French pop with a mixture of contempt and ridicule, Camille Dalmais might have been invented specifically to puncture this anglophone arrogance. In the 15 years since her debut album, Le Sac des Filles, audiences around the world have been enthralled by her vocal experiments – multitracked choral works that transform glottal stops, breathless yelps and plosive syllables into beatboxing patterns – and her closing song tonight, the a cappella Tout Dit, is a reminder of this. Now her fifth studio album, Ouï (a pun on the French words for “yes” and “hearing”), adds a riotous drum section to this one-woman choir.

‘Drums call for assembly and rebellion and dance’ … physicality is essential to Camille’s touring band. Photograph: Alecsandra Raluca Dragoi for the Guardian/The Guardian

“Drums are inherently political,” she explains to me in the Barbican dressing rooms after the show. “Drums call for assembly and rebellion and dance. They speak to the tummy. They come from the ground, and I think we, as a people, need grounding. We live in a world that is completely out of its mind. In a couple of generations most of us have completely forgotten how to grow food, how to live off the land. And drums ground us. They tell us what it is to be together, what it is to be a society.”

Everything has to go through my body. I need to feel the vibrations. It’s why I perform barefoot Camille

The sense of physicality is crucial to Camille’s touring band. “I need my musicians to embody their instruments, not hide behind them,” she says. “They have to explain the music to the audience visually.” When touring her Le Fil album in 2005 and 2006, Camille used loopers – the real-time sampling pedals used by performers such as Jamie Lidell, Tune-Yards, Imogen Heap and Reggie Watts. “I got bored,” she says. “I like repetition to be physical, like a mantra. It’s why I hate click tracks and programming and backing tracks. Urgh. It’s like slavery!”

Every sound created on stage is made physically by Camille and her sextet. As well as her Greek chorus of backing singers, there are two percussionists (who dance, theatrically, around their kits) and one keyboard player (who jumps between a Moog synthesiser and a shabby, out-of-tune prepared piano). On Home Is Where It Hurts, the band create steampunk techno, a riot of jabbering piano, rhythmic humming and clattering percussion. On Ilo Veyou, their foot-stomps and yodelling vocals forge a junkyard R&B; Paris, a bittersweet hymn to Camille’s home, is transformed into a piece of bubblegum doo-wop.

‘My movements come naturally to me. It’s not preplanned’ … Camille. Photograph: Alecsandra Raluca Dragoi for the Guardian/The Guardian

“I like to re-digest musical genres in an organic way,” says Camille. “Everything has to go through my body. I need to feel the vibrations. It’s why I perform barefoot.” The boundaries between stage and seating are also broken down. Camille brings a dozen audience members on stage to dance to Les Loups, an antique French folk melody that is transformed into a rave anthem; a dozen more are invited to form a choir and improvise a song by chanting the word “London”. During Seeds, she and her group strap snare drums to their bodies and march out of the auditorium, around the foyer and back in again, like a surreal military marching band.

Camille occasionally consults the South African choreographer Robyn Orlin to help enhance the theatrical experience. “We don’t choreograph, it’s more about space and staging. My movements come naturally to me. It’s not preplanned.” One recurring feature in this tour is a blue sheet, which Camille uses as a ghostly shroud, a mask, a ligature, a parachute, a cinema screen, a pool of water, even a womb.

“I like multifunctional things,” she says. “With childbirth you can see how your entire body is transformed into something completely different for nine months. I love how nothing is wasted in nature. Everything is multifunctional.”

This Ouï project was originally supposed to be a political treatise – a meditation on Le Pen, Trump, Brexit and environmental catastrophe. “I started writing political songs, but I didn’t want a whole album of – what’s the word? – shit-stirring. And I don’t particularly like French-language protest songs, what we call chansons engagées. I wanted to communicate on another level. The words here are playful and peaceful, not heavy. The heaviness comes from the performance.”