With its black and white photography, upbeat but muddled heroine and episodic narrative, Frances Ha has all the trappings of homage, both to those French New Wavers Godard and Truffaut, and to Woody Allen at the height of his powers.

At the same time, though, this feels like such a vital, contemporary film. Director Noah Baumbach and his star Greta Gerwig have co-written a script that speaks to a generation of young people who find the fulfilment of their ambitions frustratingly out of reach, doing so with a supremely engaging lightness of touch.

Gerwig's Frances is a 27-year-old apprentice with a dance company in New York who can't see that she's never going to be promoted into the company proper. While her vocation is stalled in first gear, her personal life – already half-boiled – starts to fall apart.

The film opens with Frances living happily with her best friend Sophie (Mickey Sumner) in Brooklyn, neither woman committed to her boyfriend, the pair "like a lesbian couple who don't have sex anymore". But then Sophie opts to move into a dream apartment in Manhattan; worse, just as Frances's impatient boyfriend dumps her, Sophie decides to up the ante with hers. Our heroine is cast adrift.

Unlike traditional scripts, this is episodic, freeform; and while we are accustomed to character trajectories that tend to move in straight lines, their fortunes rising or falling, Frances's meanders, in keeping with her personality, leaving us unsure whether to expect her ultimate success or failure.

We follow, though, entertained and enthralled, as the nomadic miss moves in with two amiable, creative chaps, typically oblivious to the fact that one of them might be ideal for her; leaves New York for a breather with her parents in Sacramento, where we witness the comfort she's had the courage to sacrifice in order to pursue her dream; then for a holiday in Paris, a catastrophic disaster played out with sublime irony to Hot Chocolate's Everyone's A Winner; to her seeming nadir, a mundane job at her old college.

Frances is lonely, desperate. But she's buoyed – as is the film – by pluck and kooky joie de vivre, expressed most rapturously in a dance sequence balanced between reality and fantasy, a tracking camera following a hurtling Gerwig along the New York sidewalk, this time to the more sympathetic soundtrack of Bowie's Modern Love.

Gerwig clearly likes to dance; she tapped to great effect in last year's Damsels In Distress. In fact, she's quite the all-rounder – her Frances is sweet, heartbreaking, funny, maddening, authentic, the actress an equal to her heroine (and Woody Allen's muse) Diane Keaton.

"I'm so embarrassed. I'm not a real person yet," Frances asserts at one point. What she doesn't realise is that she is vibrantly real; she simply has to accept that her professional calling is staring her in the face, and that what makes her "undateable" is her own misguidedness.

Frances Ha is about self-realisation, then, its breezy style allowing its truthfulness to sneak up on you unawares. Baumbach has already given us a number of finely-honed character pieces, including The Squid And The Whale and Greenberg, the latter his first collaboration with Gerwig. Here he conveys a fresh, intoxicating sense of New York (beautifully photographed by Sam Levy) confidently directs his young cast (Sumner, daughter of Sting and Trudie Styler, is an able foil to Gerwig) and juggles the emotions like a master. This could have been horribly twee; instead it's joyously entertaining.