Directed by Jean-Jacques Annaud, with sublime cinematography by Robert Fraisse, this film often gets too much attention devoted to the graphic love scenes, but is also a beautiful depiction of 1920s colonial Vietnam, and a moving love story.
Gabriel Yared composed a simple but beautiful main theme for the film, which he explains about here - https://www.youtube.com/watch?v=1bkzCX2a-Hk
The full orchestral version is sadly never heard in the final version of the film, but this scene is the first and fullest presentation, as the relationship takes its first tentative steps.
Starring Jane March, Jeanne Moreau and Tony Ka Fai Leung; and based on the autobiographical novel by Marguerite Duras. Music composed by Gabriel Yared.