Film of the week: The Illusionist, Sylvain Chomet, 79 mins, (PG)

Some cities become the ghosts of the movies that immortalised them. When we visit, we see their romance through the prism of the screen. Vienna in The Third Man. Rome in Roman Holiday. Venice in Don't Look Now. New York in Manhattan. To this list we can now add Edinburgh in The Illusionist, Sylvain Chomet's beautiful and melancholy portrait of a man out of time, which also happens to be a valentine to Scotland's capital.

That it is an animated film should not be any reason to doubt its place among those urban classics; indeed, it's hard to imagine a more exquisitely crafted picture of Edinburgh's gaunt, handsome streets, its weather, its light, even its traffic.

The French-born Chomet's previous animation, Belleville Rendez-Vous (2003), was a spikily baroque kidnap drama with a champion cyclist as its hero. His latest dials down the surreal grotesequerie and amps up the charm, being an adaptation of a script written but never filmed by comic-cum-national treasure Jacques Tati. It marks a change in mood from his Monsieur Hulot misadventures, less whimsical, more heartfelt, which is reportedly the reason why he left it on the shelf. Chomet, having negotiated with the Tati estate, could hardly have paid its creator a more loving tribute than he does here. The story, set in the late 1950s, concerns the travails of an illusionist, Tatischeff (Tati's real name), who finds his livelihood in the music-halls of Paris and London being usurped by the brash new wave of rock'n'roll ("Billy Boy and the Britoons", no less). His stage act belongs to another era, and no amount of "magic" can halt the disappearing audiences. A Tati-bye, you might say.

With only his recalcitrant white rabbit for company, he ends up travelling to Scotland to perform in a tiny pub on the Western Isles, where he encounters Alice, an innocent young chambermaid. Enamoured of his magic tricks, she follows Tatischeff when he departs for a season in Edinburgh, and the pair set up home in lodgings, like an old actor with his dresser. Change is in the air here, too, signified in the ominous newcomer on the High Street, a television and hi-fi shop. Yet, in spite of Tatischeff's narrowing circumstances, The Illusionist offers joy amid the sorrow, notably through its glorious recreation of Edinburgh – in the majestic winding lanes around the Castle, the open-backed buses tooling up and down Princes Street or the magnificent Victorian behemoth of Jenners department store. Tati's script was originally set in Paris and Prague, but Chomet changed the latter, having fallen in love with Edinburgh when he presented Belleville Rendez-Vous at the film festival. (Prague has cause to feel miffed on seeing this).

We have become rather used to the super-exact clarities of 3D animation. The argument now runs that, if you can do it on a computer, why bother with the manual labour of D? The Illusionist offers the perfect riposte. The hand-drawn graphics have a charm and individuality that digimation could only approximate. It is a little like the difference between hearing a song on vinyl and hearing it on CD. Computers offer precision, but hand-drawn brings warmth and vibrancy. As Chomet puts it, "CGI is good for robots and toys, less for humans. I want to see the work of an artist on the screen, not a machine whose visuals are too neat, shiny and clean." The retro look of Edinburgh here harks back to the Disney of the 1960s, notably London in 101 Dalmatians and Paris in The Aristocats. It's a matter of dingy pub lighting and of shop facades that our grandparents would have recognised, but it's also heard in the gurgling of ancient plumbing and the shuddering of bathroom sinks.

The sound of human voices is scarcely more articulate; Tati doesn't much care for dialogue, and you'll be pushed to hear Tatischeff or Alice mumble more than half a dozen phrases each. Much of the meaning resides in the silent comedy of body language, his a tentative craning and ducking (he's too tall for doorways), hers the bemused devotion of a young woman towards a man she believes literally capable of magic. Chomet is plainly a fan of the old guard, and one scene in which twin motorcycles are mistaken for a car is lifted almost entirely from Keaton. The sadness of the illusionist's realisation that his time is up – you may hear less bitter echoes of Olivier's Archie Rice in The Entertainer – goes deeper once Alice finds love with a man of her own age. That Tatischeff once bought her shoes and clothes suggests not so much a romantic longing as age's quixotic indulgence of youth; even his chaste love for her is doomed to failure.

The note of elegy is unmissable in the closing scenes, the camera rising and whirling giddily above the city before descending, for the last time, on the old music-hall, its lights the last to wink out. Chomet's own music provides an affecting accompaniment here. An era is drawing to an end, and its loss seems to inhabit poor Tatischeff as he sits in the train's third-class carriage, his neat suitcase perched on his knees. It may not have the same power to move as Toy Story 3 – what does? – but The Illusionist finds in the story of this gentle, self-effacing fellow a resonant truth. When an art dies, it takes some of the magic of life with it.(PG) 79 mins, Sylvain Chomet