American movies have a long tradition of insisting that characters have an arc, that we see signs of “growth” between the moment we meet someone on screen until the closing credits. We like to understand “motivations,” the things that draw lovers together after the movie has spent a lot of time keeping them apart. Life doesn’t necessarily work that way, but the movies do.

The French drama “Rust and Bone” runs roughshod over those traditions. An unconventional romance that isn’t particularly romantic, it’s about two damaged people who are pulled together even though the attraction is hard to pinpoint, the “growth” too insignificant to measure.

Ali (Matthias Schoenaerts) is poor and jobless, begging, borrowing and stealing his way to the south of France with his 5-year-old son (Armand Verdure). He tells his sister (Corinne Masiero) that he grabbed the kid because the boy’s mother used the kid to smuggle drugs. So Ali has come to stay with that sister, pick up assorted jobs working security, maybe train and get in a few kickboxing fights.

He is impulsive, irresponsible and often rough with the kid, when he isn’t ignoring him. His love life consists of the odd pick-up - one-night-stands that don’t even last a night.

Stephanie (Marion Cotillard) is an Orca trainer at a French Riviera Marineland park. She rarely smiles and seems to take pleasure in nothing.

The connection between Ali and Steph is hard to figure. They meet when he breaks up a fight that involved a guy hitting on her, and then hitting her, in a nightclub. Ali drives her home, tells her she dresses like a prostitute and insults her boyfriend. Naturally, when there’s an Orca accident and she loses her legs, she calls Ali. Here’s a brusque brute who may appeal to some oddly Gallic sense of macho in her, but who, if nothing else, won’t pity or coddle her. He treats her like every other woman, like she’s lucky to be around him, that he’s going out, going swimming, etc. And if she wants to sit and sulk in the wheelchair, that’s fine.

Ali slips into the brutal underworld of bare-knuckle mixed martial arts fights. No rules, no medics, with gambling money providing the purses. His son is never more than an inconvenience to him, and Steph isn’t even that.

Even after they’ve become intimate, it’s intimacy without kissing - strictly therapeutic sex so she can see “if things still work.” For some reason, she is drawn to him and his bloody sport. Perhaps the shock of the violence makes her feel alive again.

The Oscar-winning Cotillard, who is Angelina Jolie-thin for this film, is getting a little Oscar buzz for her performance in what is essentially a stunt. Yes, the movies have gotten very good at erasing legs below the knee. Yes, she’s convincing in the wheelchair, or wearing prosthetic limbs.

But her performance gives us so little that there’s not only no arc to follow, there are too few moments of great empathy to connect us to her. Her return to Marineland and the whale that crippled her offers an emotional highlight that is out of character with the rest of the movie.

Schoenaerts has to play Ali as even more of a mystery, a man who has no moral compass, no sense of responsibility and yet some strange compulsion to be a friend to this damaged woman. It’s impossible to gauge any growth in him, either.

This film, from the director of “A Prophet,” maintains a palpable tension between the characters. We’re never quite sure what explosions they’re capable of with each other. But “Rust and Bone” doesn’t earn the ending it delivers. And whatever its other merits, it never overcomes that initial “Let’s skip over what draws them together” handicap.

Sometimes a “subtle” connection is one the filmmaker never got around to working out himself.