Anne Consigny in “Savannah Bay.” (Nathalie Hervieux)

The notion of human beings as solo travelers is poignantly challenged in Marguerite Duras’s “Savannah Bay,” a play from France that is as freshly and lovingly cultivated as a newly mown lawn in spring.

Two unnamed women, an elderly one of faltering capabilities (Geneviève Mnich) and a younger one who acts as her helper (Anne Consigny), meet daily in a starkly white room, possibly in a nursing home, to try to recall the circumstances surrounding the tragic end of a third woman, to whom one or both were related.

The details are intentionally vague in director Didier Bezace’s flawless production, brought to the Kennedy Center’s World Stages drama festival by the Paris-based Thé âtre de l’Atelier. It isn’t so much the murky story of the dead woman — who, it seems, drowned herself a long time ago — that counts most here. It is the nourishing of the two women’s devotion that matters, as the older woman, a retired actress, struggles to recapture the past for the younger woman, who in turn strives with a touching meticulousness to keep the older one’s mind engaged.

With nods to Samuel Beckett’s co-dependent prisoners of time, Vladimir and Estragon in “Waiting for Godot,” Duras developed in this 1983 play a picture of the desire for someone else always to help us fill in the blanks. Bezace commences the one-act play — only 70 minutes long, in French, with English surtitles — with the image of Mnich at night, at the edge of the water, holding a candle. The darkness into which her character has fallen becomes clearer in the daylight, as Consigny’s character seeks to stimulate her powers of recall by having her repeat back the lyrics to a wistful song about love and regret.

Mnich, a veteran stage and film actress, marvelously conveys in the center’s Family Theater the older woman’s fragile hold on the present. (The part was originally supposed to be played by Emmanuelle Riva, an Oscar nominee for “Amour,” but she had to withdraw.) Mnich keenly evokes the childlike sense of expectation that if she waits quietly enough, an explanation will be supplied for the confounding mysteries of daily life. “I think I look beautiful,” she declares firmly as she looks into a weathered mirror that’s been set up for her, to size up the red dress she once wore for her performances.

Consigny, meanwhile, offers up an equally compelling portrait of a woman trying to reclaim her past through another’s failing memory. Was she the child born just before the woman they both speak of committed suicide? Is the older woman her grandmother? That we’re not frustrated by the elliptical quality of their conversation attests to the tender bond the two actresses manage to forge.

“Savannah Bay” — staged in a series of vignettes that, thanks to the repeated drawing of the stage curtain, seem to wade into one another, like gentle waves — touches on such cerebral issues as how memory works and, more peripherally, how we care for the elderly. It also, more whimsically, reminds us that how we choose to remember can be as meaningful as what actually transpired. But it’s most movingly an account of our collective loneliness, relieved by the benevolent impulse to share.

Savannah Bay

By Marguerite Duras. Directed by Didier Bezace. Set, Jean Haas; lighting, Dominique Fortin; costumes, Cidalia da Costa. About 70 minutes. In French with English surtitles. $49. Through Saturday at the Kennedy Center for the Performing Arts. 202-467-4600.