It's meaningless French wank, but also famous, influential and in its way kind of brilliant.
I chose those words carefully, for what it's worth. I'm not just slagging it off. "Meaningless" is the film's explicit intention and the director has said so. "Wank" implies pretentiousness and pointlessness, which again clearly apply.
The story barely exists. Giorgio Albertazzi tries to convince Delphine Seyrig that they had a love affair the year before, despite the fact that Seyrig says she's never seen him before in her life... and that's it. That's the entire storyline. Nothing happens, there are no plot developments and nothing is resolved. We never even learn the truth about what happened the previous year.
What it has instead is beautiful, ambiguous presentation of this in a manner that encourages you to engage with what Albertazzi's saying and to look for meaning in it. Reality in this film is malleable. Crowds freeze in mid-conversation while Seyrig wanders through them. There's a moment where she turns around and is teleported from one room to another so smoothly and inconspicuously that I wasn't sure if I'd seen correctly and so I rewound the DVD to be sure. There's a ton of narration, all from Albertazzi, and the film deliberately blurs the line between truth and storytelling. "Where were you? (...) I looked there too." The first thing that actually happens (about ten minutes into the movie) is that we realise we're watching a stage play, while there's a pair of statues in the garden for which Albertazzi and Seyrig invent multiple contradictory inner lives.
It takes place in a hotel that's more like a palace. Everyone wears evening dress throughout. It's polite, elegant and beautifully well-spoken.
Obviously it's heavily dependent on the actors, whom I liked. They're stylised, but that's what the film required. My next claim is going to sound silly, but they reminded me of William Russell and Jacqueline Hill two years later in Doctor Who. They have a similar air of intelligence, in which they seem at once above and utterly engaged with the material. They have a similar rapport, in which they seem immediately familiar and comfortable with each other, although admittedly we never saw Russell putting his hand on Hill's (clothed) boob. Albertazzi even looks like Russell in certain shots... there's less physical resemblance with Seyrig, who's is more movie-star beautiful than Hill, but both ladies have similarly armour-plated hair.
They'd have been a good Ian and Barbara, I think. Albertazzi does well because he's the one having to make all the running in the movie, selling a ridiculous idea to the audience (and Seyrig) and also delivering all that narration. Seyrig meanwhile has interesting transitions. Sometimes she's Barbara Wright. Sometimes she's a little girl. ("Why me?") I enjoyed watching her. There's also a man who may or may not be her husband, played by Sacha Pitoeff, who's got an interesting face.
It's a massively stylish film. Peter Greenaway has called it the most important influence on his own work, for instance, and I'm pretty sure there are points of backstory to which the only clues are the director's shooting and editing choices. I'm thinking of the over-exposed whiteouts, for instance, or the bit near the end where Seyrig walks up some stairs shot like a crypt, with church organ music on the soundtrack. Resnais's transitions are clever, so for instance we might realise we've been brought back to reality (whatever that is) with visual or sound cues so subtle that I'd need a rewatch even to identify them.
Would I recommend it? Not really. I was clock-watching and I'd have preferred it as a thirty-minute TV episode. It kept me watching to the end, which slightly surprises me in hindsight, but it's an unfamiliar kind of film and an explicit rejection of the story-focused filmmaking that has been raised by Hollywood to the level of a religion. You don't watch this film for its story. If you do, you'll go insane. No, you watch it for its Rorschach-like layers of ambiguous possible meaning and for the pleasure of watching elegance and beauty. It's a beautifully shot film in which impeccably civilised people with the finest clothes and manners discuss impossible things in a palace and its grounds. It was Oscar-nominated for Best Screenplay (eh?) and it won the Golden Lion at the Venice Film Festival, for whatever that's worth. It's style over substance, yes, but the style is flawless and the avoidance of substance is deliberate. It's also in black-and-white, so that's good too.