Leos Carax is the sly anarchist of French cinema whose sorties are sadly few and far between. Now he has broken cover with this barking mad fantasia, an almost entirely sung-through musical tragedy created with Ron and Russell Mael from the band Sparks.

Ron and Russell make their first appearance here in a recording studio with Carax behind the glass. “So, may we start?” demands the director. And start they do, with the Maels, Carax, his stars Marion Cotillard and Adam Driver and the entire cast singing as they march out of the studio and into the streets of downtown Los Angeles, ready to begin the entirely bizarre action.

Driver plays Henry, an aggressive comedian-ranter in LA with a controversial reputation and a fading career, shuffling around in the wings like Jake LaMotta in a boxer’s robe, and smoking a cigarette. He will bait the audiences with his hostile riffs and singing interludes, occasionally staging horribly tasteless Bataclan-style fake gun attacks on himself just to shock everyone.

Henry is in a relationship and in love with his polar opposite, Ann, a charismatic and exquisitely beautiful opera singer played by Cotillard. She comes from the highest of high culture, her reputation jealously protected by the opera house’s conductor. After the performance, Ann’s bad-boy boyfriend will show up outside the opera house on his motorbike and whisk her off to their beautiful home. Soon, Ann is pregnant, but she is troubled by rumours (or dreams) that aggressively macho Henry is about to be hit with a #MeToo case.

Their relationship ends with tragedy – and there is something very disquieting about their baby girl, Annette, who looks like a wooden marionette and can sing with her mother’s amazing, grownup voice. Soon, the increasingly bleary, mad and humiliated Henry devotes himself to being Annette’s full-time svengali. Any hopes we might have had that this could somehow end well are to be dashed.

Annette is a forthright and declamatory and crazy spectacle, teetering over the cliff edge of its own nervous breakdown, demanding that we feel its pain, feel its pleasure and take it seriously. We think it isn’t quite as imaginative and complex as Carax’s previous film, Holy Motors, and we were a little disappointed that there was relatively little for Marion Cotillard to do. But Adam Driver has a malign magnificence, that equine face progressively losing its nobility as he gets more violent and depressed and finally ages by about 30 years.