Jacques Audiard's new film is set in Antibes, but save for an occasional glimpse of the sea you'd never know it. The director's interest lies not in the beautiful people but with those who inhabit the frayed edges of life. He is fascinated by their sinewy determination, their guile and, above all, their recklessness. Ali (Matthias Schoenaerts), a rootless boxer with a passion for fighting, has pitched up in the resort with his small boy, Sam. At the nightclub where he works as a bouncer, he meets Stephanie (Marion Cotillard), a trainer of killer whales. He saves her from a brawl, drives her home and leaves her with his telephone number. Soon after this, something appalling happens. During a show, one of Stephanie's orcas misreads her signals; it turns on her and she loses her legs.

So far, so horrifying. Confined to a wheelchair, Stephanie calls Ali and they embark, thanks to his refusal to pity her, on a bracing and pragmatic friendship: when she wonders aloud if she will ever feel desire again, he sleeps with her, so she can find out. Meanwhile, she becomes his manager, running a book on him when he takes part in illegal bare-knuckle fights. Something about her prosthetic limbs – she has by now learned to walk again – seems to quieten the men down. It's not that no one would rip her off; rather, that she has a physical strength all of her own.

There follows a love story and, thanks to Cotillard and Schoenaerts, it somehow works. What could be melodramatic and sentimental seems fresh and true. The picture as a whole, though, is overpacked: the screenplay (by Audiard and Thomas Bidegain) groans with side plots about union rights, sibling rivalry and parental neglect – a scattered, desultory narrative that wears you down after a while and, worse, detracts from Audiard's marvellous set pieces (his handling of the Marineland disaster is exquisitely done). Afterwards, I wondered why the director seemed to have lost faith in his own story. Had it to do with misdirected artistic pride? Perhaps.

There are scenes in Rust and Bone that seem, on paper, to have come straight from the sugar mine that is Hollywood: Stephanie dancing to the B-52s in her wheelchair; Stephanie returning to Marineland to commune with the whales. It's possible that Audiard simply couldn't bear not to bound them with a little light violence and added social realism. But, whatever happened, it's a pity. Cotillard is the beating heart of this film; she's all you need. As she leaned on her stick with one hand and tapped on the glass of the orca's pool with the other, I didn't groan, as I might have done in another movie. I held my breath at the audacity of the moment and waited for the creature to appear, its vast shadow falling like a benediction.