Jacques Audiard pulls off a distinctly different sense of tone and timing from his last two acclaimed award-winning films, “A Prophet,” and “The Beat My Heart Skipped,” in this raw love story between Matthias Schoenaerts as a directionless single father, who makes money by competing in illegal boxing matches, and Marion Cotillard as a killer whale trainer, who loses her legs in an on-the-job accident.

It’s definitely not a “meet cute,” when Schoenaerts’ Alain first encounters Cotillard’s Stéphanie (pre-accident) at a night club in Antibes in southern France. Alain (“Ali,” to his friends and family) is on his first night as a bouncer at the club when a fight breaks out and Stéphanie, dolled up for a night on the town, gets caught in the middle of it.

Acting the gentleman, Ali insists on driving the roughed up Stéphanie home to her apartment, only to find that she has a controlling abusive boyfriend waiting for her there. Nevertheless, Ali gives her his phone number – “if you need it” – before exiting.

Not long after that, the vividly scary spectacle of a large Sea World-type stage collapsing during an Orca show (to the tune of Katy Perry’s “Firework,” mind you) leaves Stéphanie without legs below her knees, via seamless CGI that shows us how far such special effects have come since Gary Sinise’s similar predicament in “Forrest Gump.”

In the midst of her painful recuperation, Stéphanie decides to call Ali, who’s by then working as a guard at a security firm. The stoic strongman begins taking care of the legless lady, and in a sweet scene set at the beach, he carries her into the ocean and she appears to have a cathartic experience wading in the sundrenched waves.

Stéphanie gets close enough to Ali that she even accompanies him on his street fighting ring runs, but has to stay in the car as women aren’t allowed. Ever so casually, while cleaning up after a meal, Ali asks Stéphanie if she wants to have sex. Embarrassed by the bluntness of the proposal, yet intrigued, Stéphanie agrees and afterward she appears regenerated, on her way to feeling whole again. An immersive shot in her empowering post-coitus sequence shows Stéphanie, now outfitted with prosthetic legs, visiting her old workplace and reconnecting through body language with the enormous whale that caused her accident through a giant glass partition.

Unfortunately, Ali continues to see other women, and his relationship with Stéphanie suffers. What also suffers, albeit only slightly, is the movie’s focus in its second half as its storyline gets messier than it needs to be. Especially when Ali’s sister (Corinne Masiero), who is taking care of his 5-year-old son (Armand Verdure), loses her job because of video surveillance set up by Ali’s company. This causes Ali to leave town, leaving everything up in the air with Stéphanie.

The brooding Schoenaerts, previously best known for his leading role in Michael R. Roskam’s 2010 crime drama “Bullhead,” has such a dry, cold demeanor that his character can be hard to relate to, but edges of humanity come through at crucial moments, particularly when he realizes late in the game his feelings for Cotillard’s Stéphanie.

Cotillard, displaying comparable poise and power to her incredible Oscar-winning portrayal of Édith Piaf in “La Vie en Rose,” owns the heart of “Rust and Bone.” She wasn’t nominated for an Academy Award this time around (and she lost the Golden Globe for the part to Jessica Chastain for “Zero Dark Thirty,” earlier this week) but she’s taken home a few well deserved awards for the performance (at the BFI, Cabourg, and Telluride Film Festivals).

Audiard’s “A Prophet,” cinematographer Stéphane Fontaine captures the couple, and the sunny scenery surrounding them in a visual style that’s often poetic. Based on a short story collection by Canadian author Craig Davidson, Audiard’s screenplay, co-written with Thomas Bidegain, keeps the dialogue spare and simple, which helps it stay clear of clichés.

In this random romance, in which tough times tinged with tragedy can bring disparate damaged people together, Schoenaerts’ thick-headedness and lack of sentiment can numb one’s heart, but Cotillard’s longing and belief in love will melt it.