La Moustache opens with Marc Thiriez, a middle aged Parisian, asking his wife if he should shave off the moustache he has sported for most of his adult life. His wife, Agnes, wrily comments that she wouldn't recognize him without it, yet as she leaves Marc shaves the moustache off. Upon her return, Marc asks his wife if she notices anything. She does not respond. A day passes and he then asks his wife is she has noticed that he has shaved off his moustache. She tells him that he hasn't had a moustache in years. What follows is a moment of catharsis-Marc is told that his father is dead, that his best friends do not exist, and he soon learns that his wife wants to have him institionalized. In a moment of panic, Marc flees the country and travels to Hong Kong.

The movie's resolution is unclear, as is the movie itself. La Moustache captures an element of suspense, though the actions and plot are ambiguous. Many critics have said that the film's events are not literal, but metaphorical and are symbolic of Marc's loss of identity (of a possible mid-life crisis).