Jacques Audiard’s “Dheepan” is named for a man who is not what he appears to be. Dheepan is a Sri Lankan refugee working as a handyman in a crime-ridden French slum — that much is true. He has a wife and a preteen daughter, but they, too, are fictions. In fact, they all met only recently. “Dheepan” tells the story of a pretend family whose best chance of survival is to somehow become a real one.

Dheepan, played by Jesuthasan Anthonythasan, may speak Tamil and French, but he’s a character American moviegoers will recognize. Like Viggo Mortensen’s Tom Stall in “A History of Violence,” Dheepan is The Family Man With a Dark Past. Here in France, Dheepan looks like just another immigrant keeping his head down among thugs and drug-dealers. Little do they know he’s a former soldier in the Tamil army — an unsavory association he has hidden from France’s immigration officers.

Anthonythasan, himself a former Tamil fighter now living in France, is thoroughly convincing as Dheepan, a taciturn man with a rough beard and a soft heart. He feels a duty to the orphaned Illayaal (Claudine Vinasithamby), who poses as his daughter; in a series of small and very touching scenes, the two silently allow fiction to become a reality. Only Dheepan’s young “wife,” Yalini (an excellent Kalieaswari Srinivasan), refuses to settle into her role. She dreams of joining her real relatives in England, and flirts with a local crime boss, Brahim (Vincent Rottiers, charming and chilling).

“Dheepan,” which won the Palme d’Or at Cannes, is not quite the thriller it claims to be. The tension between Dheepan and the locals promises a climactic catharsis along the lines of “Unforgiven” or “Cop Land,” but the climax arrives with little fanfare. This seems intentional — Audiard obscures the carnage in a haze of smoke reminiscent of Dheepan’s burned-out homeland — but it also lessens the movie’s impact. The arc of an action film gives “Dheepan” a narrative shape, but it isn’t wholly necessary. Audiard’s characters, and his fine cast, can stand on their own.