This is Rohmer's openly Pascalian film, in which the mathematician Blaise Pascal (1622-62) is mentioned several times. Jean-Louis (Jean-Louis Trintignant) is an engineer who has recently worked in Canada and South America and now is based in Clermont-Ferrand working for Michelin: many years before, Pascal was born in what was then just known of Clermont.
Jean-Louis goes to a bookshop and buys Pascal's Pensées. He is Catholic, handsome and unmarried: he has had a number of relationships which have led to nothing concrete, and then in Clermont cathedral he sees a young woman he will later know as Françoise (Marie-Christine Barrault), a blonde, with whom he becomes infatuated, to the point of trying to follow her 'mob' until he loses her. This is Christmas and people are celebrating, he goes into a café-restaurant and bumps into Vidal (Antoine Vitez), whom he has not seen for a number of years.
Previously, there was talk at Jean-Louis's workplace of a man who has narrowly avoided death on the local icy roads. This recalls the mishap Pascal had had in 1654 on the Pont de Neuilly, when he had a near-death experience while in his carriage. Vidal is a university lecturer of philosophy and they talk of Pascal's bet, although as a Marxist Vidal sees the bet in historical as opposed to religious terms.
Led to the flat of the separated doctor Maud (Françoise Fabian), the three have a meal and speak of Pascal, although Vidal has too much to drink and leaves. The snow outside prevents Jean-Louis – who speaks of the blonde girl he's seen as if she were a positive entity in his life – from leaving, and although he sleeps at the side of Maud, and although Maud entices him several times, he makes no attempts to have sex with her.
By chance Jean-Louis meets the Catholic moped girl again, entreats her to meet him, gets stuck in the snow taking her home, sleeps in her spare room, walks with her on the heights of Clermont, although she resists his advances.
Flash forward five years and at a beach people again chance upon one another, but Jean-Louis, Françoise and their young son meeting Maud is a very unusual coincidence, especially as Françoise knows Maud because she's had a relationship with her husband. Such are the games Rohmer loves to play.