French writer-director Claude Sautet, who died in 2000, is famed for chronicles of bourgeois life, many of them rather sappy. Some U.S. filmgoers know that he unexpectedly switched to an icier, more trenchant style for his last few movies—notably the superb Un Coeur en Hiver (1992) and Nelly & Monsieur Arnaud (1995)—even while keeping them set firmly in the domestic sphere. What’s less known, thanks to the vagaries of foreign-film distribution, is that Sautet’s early work explored a rather different demimonde.

After serving as assistant director for such pre–New Wave filmmakers as Jacques Becker and Georges Franju, Sautet finally got to make a film of his own: 1960’s Classe Tous Risques (roughly, “The Big Risk’’), a transition piece between traditional ’50s gangster flicks and the cooler ’60s style of Jean-Pierre Melville. The last championed the movie, but it flopped commercially, only to become a success in France upon its 1971 reissue. In the United States, Classe Tous Risques remained largely unknown, awaiting the Rialto Pictures treatment: refurbishment and reissue, with new subtitles, by the New York distributor that brought us Becker’s Touchez Pas au Grisbi, Franju’s Eyes Without a Face, and Melville’s Le Cercle Rouge.

Sautet was influenced by Italian neorealism, and he originally intended to set most of Classe Tous Risques in Milan. But the producers insisted on the trans-Europe escape detailed in the source novel, written by José Giovanni, so the movie departs that city in a hurry, heading for France. Two gangsters who can’t take the heat in Italy anymore, Abel Davos (Italian-born French actor Lino Ventura) and Raymond Naldi (Stan Krol), decide to do one last job and skip the country. They put Abel’s wife and two young sons on a train to a border town, stage a rashly conspicuous daylight street robbery, and then head for the rendezvous by car and motorcycle. A few reversals later, two of these characters are gone, and Abel and his boys are hiding out in Nice, waiting to be rescued by the thug’s old comrades, Riton (Michel Ardan), Raoul (Claude Cerval), and Jeannot (Aimé de March).

In what turns out to be the story’s thematic hinge, those comrades refuse to come. Instead, Abel’s cautious pals send a dashing young freelancer, Eric Stark (Jean-Paul Belmondo), who drives a bandaged Abel to Paris in an ambulance. The two men prove to be kindred souls, although not so kindred that Eric doesn’t stop along the way to rescue a pretty actress, Liliane (Sandra Milo), who quickly becomes his girlfriend. Broke, angry, and, by his code, dishonored, Abel hides in a maid’s room rented by Eric and plots his next move. He needs money and a permanent home for his kids, and he craves a showdown with the old pals who wouldn’t risk their semilegit positions for him. But the desperation that drove Abel from Milan besieges him again in Paris, personified by private detectives and brutal cops.

Released the same year as Breathless—and despite making prescient reference to Pierrot le Fou, a character later appropriated for another landmark Godard/Belmondo film—Classe Tous Risques must have seemed like an old-fashioned genre picture by comparison. Seen now, the movie looks much fresher than it probably did then. One of Belmondo’s first starring roles and a rare film in which Ventura wasn’t a second-tier player, Sautet’s movie offers a lively gallery of faces in which the beefy Ventura and thinner but hardly delicate Belmondo have a physical compatibility that seems to explain their instant rapport. And the use of actual locations—neatly framed by an opening in Milan’s Central Station and a closing set on Paris’ Boulevard des Italiens—gives the story an immediacy it still retains.

Most distinctively, the movie avoids a final confrontation, allowing Abel simply to melt away as a narrator summarizes his fate in two sentences. There’s no escape or release, either psychologically or dramatically—which, come to think of it, is why Classe Tous Risques may not be a genre flick at all.