“Never trust the teller,” D.H. Lawrence famously intoned, “trust the tale.” We’re all familiar, to one extent or another, with variations on this truism. Conversely, there’s no shortage of bromides advocating for the opposite tack. Wasn’t it the Rolling Stones who told us that it’s the singer, not the song?

The truth lies somewhere in between. “Skies of Lebanon,” the first feature by director Chloé Mazlo, juggles the dynamic between teller and tale by purposefully dropping the ball from time to time. The story is close to Ms. Mazlo’s heart, as it is based on her grandmother’s recounting of life in Lebanon before and during the country’s civil war. It’s the how of the picture in which the boundaries between biographical memory and cinematic fiction are kaleidoscoped.

The origin story of our heroine is fleetingly rendered. Alice (Alba Rohrwacher) is a dutiful daughter of the Swiss working class, a stalwart student who, upon receiving her diploma as a childcare provider from the local convent, proves not so dutiful. After applying for work as a nanny, she considers only those positions that will take her far from home. A letter arrives offering a job in Fribourg and she eats it along with the accompanying envelope, destroying the evidence. An offer from Beirut, though, that’s a done deal.

This segment of the film is rendered with clay figures and stop-motion animation, a herky-jerky unveiling of character and intent. Upon following Alice to Beirut, Ms. Rohrwacher and the rest of the cast are superimposed upon a retro-universe poached from circa-1955 travelogue films and thrift store postcards. When a Lebanese astrophysicist, Joseph Kamar (Wajdi Mouawad), woos Alice under starry skies, the setting is as artificial and contrived as the alien landscapes seen in the original “Star Trek.”

Ms. Mazlo ultimately settles on a less higgledy-piggledy approach to story-telling. That doesn’t mean “Skies of Lebanon” turns conventional. The film’s color palette is dominated by strong tones that seem to have been uniformly bleached. There are isolated moments in which figures reach out from photographs or disappear into walls. The civil war is presented as a series of vignettes featuring men wearing animal masks: Think the Keystone Kops meet Ubu Roi. The allusion between our heroine and that other Alice — you know, the one who fell down the rabbit hole — is made fairly clear.

All of which sounds horribly whimsical, like the kind of wink-wink artifice Wes Anderson fabulates in his sleep. The last thing any of us need is more postmodernist caprice — until, of course, someone comes along and proves it more palatable than our expectations might lead us to believe. Although Ms. Mazlo doesn’t altogether avoid the pedantic or coy, she’s put together a movie of genuine sweetness, a fairy tale in which family, love, and common sense survive the paranoia, fear, and separation that stem from war.

The movie is boosted considerably by the talents of Aurélien Maillé, Marios Neocleous and Alexia Crisp-Jones, respectively the production designer, art director, and costume designer, each of whom help to create a storybook world of almost Victorian plenitude. Hélène Louvart’s cinematography invests every scene with the graininess of a vintage family photo album, and the actors, especially Mr. Mouawad, simultaneously ground and vivify Ms. Mazlo’s flightier quiddities. 

“Skies of Lebanon” is the sort of off-center fable that tends to fly under the radar. Best to keep an eye out for it.