Catherine Deneuve, still stunning at age 70, is the subject, object and raison d’etre of  On My Way, the second feature film directed by French actress Emmanuelle Bercot. It’s a testament to her loveliness then and now. One of the first images in the film is a grainy black-and-white photo of a young Deneuve donning a sash; her character, Bettie, was a regional beauty queen in the ‘60s, a title that never landed her anywhere or anything. These days, she’s a widowed restaurateur who lives with her mother and whose lover has just rejected her. She has one daughter with whom she almost never speaks.

During a solitary walk on the beach, the memory of her beauty-pageant days flits across her consciousness like a passing insect, and for good reason: She’s been asked to lend her current looks to a nostalgic calendar honoring other French beauty queens from the period. She doesn’t want to accept, but she’ll have plenty of time to change her mind. About 20 minutes into the film, Bettie drives off into the bucolic countryside, unplugging from family and friends and resulting in a sometimes fascinating, sometimes somnolent series of vignettes that form the lion’s share of On My Way.

Among the highlights: She has a poignant conversation with an elderly man who rolls her a cigarette she isn’t supposed to smoke; she watches a husband beat his wife in a restaurant, only to find her assistance rebuffed by both; she has a one-night stand with a scrappy young cougar fetishist. The aimless road eventually leads to her estranged daughter and her adorable grandson, and some unexpected bonding.

Liberated from traditional movie structure, On My Way is best when it, like Bettie, doesn’t seem to know where it’s going—the magic and the mystery are in the ramble of the open road. But eventually, as the film settles into a familiar comfort zone, it becomes increasingly less interesting, with its overlong final act wrapping everything up in an implausibly perfect package. But at least we always have Deneuve to admire, in a role that, for a change, is as meaty as it is lovely. “You’ll be beautiful in your coffin,” Bettie’s daughter says, with the right balance of jealousy and sarcasm. Ain’t that the truth.

At the Broadway, SLC.