John Travolta’s directorial debut turns out to be a rather charmingly quirky and distinctively peculiar novella-sized bedtime story. It is an hour-long novelty feature commissioned by Apple TV, with lovingly detailed but innocent Mad Men 1960s period production design, and narrated throughout by Travolta itself.

That’s an indulgence you have to get used to – but if Alec Baldwin was doing it, you might almost think this was a Wes Anderson movie. It is in fact based on Travolta’s own children’s book about his love of planes: an autobiographical tale about Jeff, an eight-year-old boy, weirdly resembling the kid in the spoof classic Airplane!, who gets to overhear some pretty ripe adult conversation in a plane cockpit.

Jeff becomes entranced with aviation in 1962 after taking an all-night flight to LA with his cocktail-quaffing divorced mum on an impossibly glamorous TWA propeller plane, a “one-way night coach” already attaining its own kind of retro prestige by virtue of the jet plane’s recent invention.

Clark Shotwell plays Jeff; Kelly Eviston-Quinnett plays his mum and Ella Bleu Travolta, daughter of John, plays Doris, the 21-year-old stewardess (as they were known in those days) who takes a kindly interest in Jeff. (The film suggests she actually went on to marry him – quite the age-gap story, which perhaps needs a film of its own.)

Jeff is saucer-eyed with excitement about the whole thing, while his mum is herself pretty jazzed about the possibility of meeting a nice divorced man on the flight – and in fact there is no lack of silver-fox types onboard ready to buy his mother a Manhattan. She is of course smoking on the plane in a way that was normal until much later than the 1960s.

Another type of movie – one with the feel of a John Cheever or Frank O’Hara story – would have contrasted Jeff’s rapture with something delusional and compromised in his mum’s love life or her professional life: she is an actor, headed for Hollywood in the hopes of stardom.

Yet when Jeff and his mum have to make a hotel stopover and Jeff glimpses his mother coming out of someone’s room, it is not supposed to constitute a loss of his innocence. Jeff appears to know roughly what’s happening and treats it with no more than a shrug.

A sweet, odd diversion – more eccentric, maybe, than Travolta intended.

• Propeller One-Way Night Coach screened at the Cannes film festival and is on Apple TV from 29 May.