Once a thug, later a teddy bear: Something about brutish French actors fares less well than other Gallic exports once they become international commodities.

Take Jean-Paul Belmondo. Iconographic in Jean-Luc Godard’s “Breathless” (1960), he was a self-parody by “L’As de As” (“Ace of Aces”) 20 years later. Gérard Depardieu has had a much more consistent career, impressive in that he was never one of those scrawny cheekbone actors, lost in a cloud of narcissistic regard as thick as the smoke from their Gitanes. His face is broad and beak-nosed, and he hauls about a wrestler’s body, more hulk than hunk. How, then, did he ever wind up in Hugh Grant’s shoes, playing opposite Andie McDowell in Hollywood fluff like “Green Card”?

This month, the Film Society of Lincoln Center offers multiple perspectives on Mr. Depardieu, tough, tender and otherwise — even the French film industry lured the actor into period drama fluff like “Cyrano de Bergerac” (1990) and “Tous les matins du monde” (1991). The series, which runs through August 19, offers 20 films from the actor’s more than 170 screen appearances. Here are four not to miss.

“GOING PLACES” (1974)

Director: Bertrand Blier
Thug factor: Medium

As a deadbeat vagabond wandering France with his sidekick (Patrick Dewaere), Mr. Depardieu is the essence of petty criminality and predatory sexuality — even his buddy isn’t entirely safe. This male-bonding frolic of a picture was controversial for its time but won a champion in Pauline Kael.

Teddy bear factor: High

Despite his aggression, beautiful women submit to Mr. Depardieu’s needs. Miou-Miou, Jeanne Moreau, a teenage Isabelle Huppert, and Brigitte Fossey (as a nursing mother on a train who finds two new mouths to feed) all fall prey. There must be something they connect with, even if it’s childish ineptitude.

“MAÎTRESSE” (1976)

Director: Barbet Schroeder
Thug factor: Low

Mr. Depardieu returns to his familiar role as a low-rent thief (this one moonlights as a plumber) in this dark comedy. As tends to happen, his intentions are undone by a woman. Bulle Ogier is the dominatrix who enlists him in her body of work after he fixes her pipes.

Teddy bear factor: High

The film’s depiction of extreme sadomasochism caught flak from censors, but it’s basically like most love stories. Who’s the boss? It’s not Mr. Depardieu’s character.

“LOULOU” (1980)

Director: Maurice Pialat
Thug factor: High

Mr. Depardieu reunites with Ms. Huppert in a daring film about how obsessive sexual desire shatters the social construct. Hmmm, how French is that? Once again, he’s a lout without much going for him but somehow wins the physical and emotional affections of a glamorous woman. Why does Ms. Huppert’s bourgeois housewife throw it all away to bask in his sullen gaze? Pialat was always keen on such puzzles, which are never solved so much as scattered about.

Teddy bear factor: Low

Even a slacker has to pick up the check sometime.

“POLICE” (1985)

Director: Maurice Pialat
Thug factor: Medium

Mr. Depardieu usually did his best work with Pialat, who never lost his edge (unlike another of the actor’s frequent employers, Mr. Blier). “Police” is a gripping story in which Mr. Depardieu’s often crushing physicality yields with growing poignancy to his interior sensitivity, as a hard-boiled and ethically creative cop who goes to smash an Arab-run drug ring.

Teddy bear factor: Low

His romance with a gorgeous female drug dealer (Sophie Marceau) is of the tormented love-hate variety (scripted by Catherine Breillat, no less), so although their scenes revel in a dewy-eyed pas de deux of souls aflame on Satan’s spit, it’s none too cuddly.

Through August 19 (70 Lincoln Center Plaza, at Broadway at West 65th Street, 212-875-5601).