Advancing age and retreating inhibition now make me liable to cry at the movies. But this has to be the first time I have actually wept tears of joy. It is not high camp exaggeration. This happens every time I watch the last sequence of this exquisitely judged, gloriously funny and achingly tender film by the French director Michel Hazanavicius, a movie about the black and white silent age of Hollywood, which is itself in black and white, and silent – or almost silent. There are some spoken words, and a continuous orchestral score by Ludovic Bource.

Since seeing The Artist at its Cannes premiere earlier this year, I have become one of a global legion of jabbering evangelists, and only the fear of causing a backlash deters us from going on about its artistry more. The debonair comedy and pastiche are worn with airy lightness; the romance is gentle and yet unexpectedly passionate. It is an utterly beguiling love story and a miracle of entertainment, which unexpectedly says a good deal about male pride and emotional literacy. It even, in its insouciant way, touches on the question of whether the art of cinema was purer when it was silent.

The story is a variation on a theme from A Star Is Born. An older, established star helps a talented young woman on the path to fame, only to see his career decline as she hits the big time. It is a flirtation in which the man is teacher, mentor and lover; in The Artist it is a love made impossible by fate and the reversal of status. Physical consummation is irrelevant: the transactions of power and celebrity involved are sexier than sex.

It is 1927, and George Valentin, played by Jean Dujardin, is a dashing and lovably preposterous silent movie star, endowed with hyperreal handsomeness and eyebrows and moustache resembling strokes of a cartoonist's pen. His trademark is always to appear on screen in the company of his adorable little dog, Uggie, also an offscreen buddy as resourceful and courageous as Lassie. Valentin is, of course, a little like Rudolph Valentino, perhaps most obviously in his preferred role of mysterious adventurer, and also like Gene Kelly, in the openness of his toothy smile. He also, in his top hat, white tie and tails, very much resembles Maurice Chevalier.

Valentin is at the top of his game as we find him at the rapturous opening of his new movie A Russian Affair, a politically slanted story in which he appears to be playing an aviator and soldier of fortune battling for Georgian independence. The Russian baddies are seen torturing his character in the opening scene, with electrodes fitted to his skull, trying to make him talk. But he will not talk, thus setting the scene for stubbornness, reticence, personal vulnerability and fear of the future. Amid the cheering crowds outside, a pert little ingenue somehow blunders past the police line and winds up kissing Valentin on the cheek, to the photographers' delight.

This is Peppy Miller, played by the Argentinian-born actor Bérénice Bejo, who also appeared opposite Dujardin in Hazanavicius's 2006 spy spoof OSS 117: Cairo Nest of Spies. Their flirtation, and her infatuation with him, earns her a break in pictures, and this beautiful and good-natured young woman succeeds in impressing George's glowering producer Al Zimmer (John Goodman) and also his shrewd, loyal chauffeur Clifton (James Cromwell). But George himself is no cheater and sleazeball; he is married, albeit unhappily, and so an affair is not to be. And crucially, Peppy embraces the new technology of the talkies while he grumpily rejects them as a mere fad. She is on the upward escalator of success, passing George heading inexorably down: yesterday's man.

Everything about The Artist comes as close to perfection as I have ever seen: especially the sequence near the beginning where we see successive takes for a scene in which Valentin has to dance briefly with Peppy in his movie's "gentleman's excuse-me" party scene. First it is merely awkward, and then they repeatedly ruin the shot by corpsing, laughing more and more uncontrollably each time. (The extras' bemused, submissive smiling is superbly captured). And then the scene is abandoned, because they are looking at each other with deadly seriousness, realising something important. They have at this moment fallen in love.

George is temperamentally averse to talking. His wife begs him to talk to her at the nadir of their relationship but he will not, and his pride will certainly not permit him to discuss the possibility of trying to restart his flagging career in the talkies, in which he has lost his crown. But it is not merely this: George, in his muddled and hotheaded way, believes talkies are just crass, and that he is an artist. Silence is art: what counts is spectacle and the ecstasy of seeing. And the movie quixotically takes George's side by being silent, with intertitles for dialogue until the very end – when George says something that reveals another reason for his unwillingness to be heard, and also about the European roots of Hollywood Americana.

What a wonderful picture this is: one of those films you yearn to watch again and again, while yet being fearful of spoiling the experience. It is one of the most eloquent movies imaginable.