Nue propriété is French for bare ownership/property, i.e., without usufruct. In the film a woman considers selling the house in which she lives with her twin sons. The sons oppose this. They get support from their father, who claims bare ownership of the house, and wants to keep it for the twins.
Plot
Two young adult non-identical twin men, François and Thierry, still live with their mother. They are very close, e.g. they bathe together and wash each other's hair.
They are very upset when their mother wants to sell the house. The situation gets tense and the mother leaves the house for an indefinite time. The good relation between the twins deteriorates. In a fight one gets very badly injured. The other panics and feels guilty.