Seamless, frictionless and pretty much flawless, Max Ophüls’s 1950 movie version of Arthur Schnitzler’s racy 1900 play is rereleased as part of a campaign to save London’s Curzon Mayfair cinema; it takes its audience on a dizzying swirl, like a waltz, or a champagne-induced headspin.

The film is an ensemble or portmanteau movie set in early-20th-century Vienna, composed of 10 scenes and 10 couples, connected in a daisy chain of sex. A bighearted streetwalker has sex (for nothing) with a soldier who then dates a shopgirl, who then gets a job as chambermaid and is seduced by her employer’s grownup son, who then has an affair with a married woman, and so on, up the social class – until a bleary count is confronted by the prostitute we saw at the beginning, and is assailed by the strange sense that he has seen her somewhere before. And so he has, in a way; they are all connected, he has perhaps had an encounter with her before, or someone like her, and she has met someone like him. They are all linked in a dance of cynicism and secrecy. (I can’t help thinking of the 1920s song: “I danced with a man who danced with a girl who danced with the Prince of Wales.”)

There’s a raft of stylish performers here, including Simone Simon, Danielle Darrieux and Serge Reggiani – but first among equals is the dapper and droll Anton Walbrook as the all-knowing narrator and master of ceremonies, who spins jauntily around on his symbolic carousel, taking discreet servant roles in many of the vignettes. He also breaks the fourth wall and shows us that this is simply a movie, showing us the lights, the background set painting, the musicians. It is Walbrook who drolly “censors” a sex scene by snipping film, and when one callow young man suffers erectile dysfunction, Walbrook’s carousel suffers a significant breakdown, grinding to a halt.

But these self-references are anything but Brechtian. They are not there to distance you from the action or undermine its putative reality; they merely show that everything is all bound up in the same “ronde”, the same dance: shopgirls, aristocrats, art, illusion, cinema, life itself. Ophüls’s camera glides weightlessly from one scene to another.

The final taste that this film leaves behind is a kind of sadness-hangover. We learn nothing substantial about any of the characters, other than their willingness to cheat. But yearning for monogamy is inimical to the dance of delicious adventure. A modern audience might wonder what Arthur Schnitzler’s own experience was, and whether the licentious world of Viennese cafe society and its hookups really was so exclusively heterosexual. The film passes like a strange and tantalising dream.

• La Ronde is released on 8 September in UK and Irish cinemas.

• This article was amended on 8 September 2023 to replace the picture, which in an earlier version was of another film.