This movie is about Hélène (Sandrine Bonnaire). She is Corsican. She is slender. She is right in the middle of that period of life that forms the bridge between youth (dawn) and old age (dusk). Her youth was clearly unexceptional, and it's doubtful that her final years will be any different.
The fire has long left Hélène's marriage; indeed, it's hard to imagine that she and her husband, Ange (Francis Renaud), ever felt the flames of desire, ever kissed wildly, passionately, madly. This cold Mediterranean marriage somehow produced one child—a night, a little moonlight, a sudden kiss, a quick fuck, a deep sleep, a long pregnancy, a painful birth, a loud baby, an even louder girl, and, finally, a bitter teenager. The source of the young woman's bitterness is the position her parents occupy in the class spectrum: exactly between poverty and middle class. Her father paints boats and is broke all of the time; her mother is a cleaner at a local hotel and is working all of the time.
The mother also cleans the house of a rich and educated American, Dr. Kröger (Kevin Kline). French-speaking Kröger is the second of two important Americans in the film, the other being an unnamed woman played by Jennifer Beals ("In a world made of steel, made of stone..."). The role of the first American is to initiate Hélène's transformation; the role of the second is to complete or realize this transformation. The first American offers Hélène two possible paths to a new (or renewed) life: One is chess and the other is a sexy dress. The sexy dress goes nowhere, but the chess, with the aid of Kröger, does take Hélène all the way to a happy ending.