Catherine Deneuve, left, and Nemo Schiffman in On My Way (Film Society of Lincoln Center)

Filmmakers like knocking Catherine Deneuve, now in her sixth decade as an above-the-title actor, down several pegs, stirring ripples underneath her deceptive composure. Her characters have had it rough lately, and she’s kind of a prime target to take down as the face of French cinema—at least in this country. François Ozon recently put her through her paces as a scorned well-heeled wife-turned-industrial big shot in the smart boulevard comedy Potiche. And make no mistake, Deneuve embraces the challenge. She’s game for every detour thrown her way in actress-director Emmanuelle Bercot’s roaming road trip On My Way.

A viewer doesn’t have to be familiar with Deneuve’s long list of credits for the role of Bettie to resonate. The late-middle-age former beauty queen lives in the sticks of Brittany and impulsively takes a roundabout trek through France, with little money and destination unknown. The news that her married lover has left her for a 25-year-old woman, whom he’s impregnated, causes her to high tail it, leaving unattended her cozy seafood bistro and nosy mother. (The film relies much more on freewheeling interactions than scenery. It’s 10 percent travelogue, 90 percent droll observations.)

Those who have seen Deneuve when she was the definition of an art-house goddess will probably bristle when a much younger one-night stand marvels that Bettie “must have been stunning” when she was younger. Or when she’s called fat by a drunken ruffian. Throughout her journey, Bettie wears an off-the-rack blowsy leopard print blouse, in contrast to the actress’s longtime association with the House of Saint Laurent. Nevertheless, for those new to her work, the movie serves as a very good introduction, as well as for Bercot (Backstage), especially for those who like their road trips taken without a rigid itinerary or map.

If any company paid for product placement here, it’s Lucky Strikes cigarettes. Stressed out, Bettie breaks down and starts to light up again. Nicotine’s the only motivation that makes her turn right or left on a country highway on her search for a pack on a Sunday. In one of the funniest scenes, she barely holds it together, struggling to remain patient as an elderly man very carefully, thoughtfully, but ever so slowly rolls a cigarette for her. It’s just as well that this film is unrated by the MPAA, since it’s hard not to nod in sympathy with the observation that “a little cigarette does you good.” It would automatically get slapped with a tough R rating.

It’s as though both the director and Deneuve have heard the too-glib takeaway that the actress’s on-screen persona is icy, because, man, does she loosen up. She’s literally knocked about and not immune to the elements but left drenched, stranded in the rain in the middle of nowhere—and Bettie soldiers on. Credit is also due to the script, which gives Deneuve a multifaceted role, and a strong supporting cast (along with a few nonprofessionals). The film is also a reminder that an important component of her filmography has consistently been the lack of fear in tackling such roles when the challenge arises.