Jean Fournier (Claude Mann) has a menial job in a bank in Paris and his friend Caron (Paul Guers) has just bought a new car and has a great deal of money: he reveals that he has won the money gambling at the casino, and tells Jean that he ought to do the same, that winning money is easy. Although La Baie des anges is very different from Demy's better known films, it nevertheless contains two elements present in them: chance, or the aleatory nature of life, and fantasy, or the world of dreams.
Jean is very dubious about Caron's idea, although he's also tempted. He's far more cautious than Caron, although he decides to go the casino in Enghien-les-Bains in Ile-de-France. Jean, who lives with his widowed father, makes a good profit and tells his father about it, although his father (obviously a staunch Catholic judging from the pictures on the walls) is angry. He's further angry by Jean's choosing to go to the Côte d’Azur for his holidays instead of Loiret as usual.
And Jean finds a very different world there, not just of casinos but of one particular, beautiful and fascinating platinum blonde, Jackie Demaistre (Jeanne Moreau). Gambling is her addiction and she isn't even put off by losing: she would even lose her last franc and spend the night on the streets than not gamble her money. Jean, ever cautious (only less so) becomes drawn into her web of fantasy and madness, they get rich, buy a flash car and expensive clothes, go to a luxurious hotel in Monte Carlo and lose their money again.
The main problem is that Jean feels like a puppy dog to Jackie, although she says he's her good luck charm, her horse. In love with Jacky and unable to understand why she seems incapable of reciprocating it, he leaves her at the casino table but she runs after him.