What kind of narrative techniques does Godard use? How does this film tell its story? And to what extent does it do other things than just telling a story? What are Godard's means of presentation and digression, how do they fit together, and what do they accomplish?
What do you make of Anna Karina's performance in the lead role? How is she regarded by the camera, by Godard, and by us in the audience?
This is a film that is very self-conscious; it makes us aware of the movements of the camera, and of the manipulation of the soundtrack. Consider the moments, for instance, when the sound is cut off, or when the ambient sound of the street or the cafe is replaced by a song, or when the dialogue is conveyed in subtitles while music plays; and consider how the camera moves, how it seems autonomous, rather than following the logic of the characters. What does Godard accomplish by structuring his film in such a way?
At one point in this film, Nana goes to the movies, and watches Carl Theodor Dreyer's great silent film The Passion of Joan of Arc. At another point, a man reads to her a short story by Edgar Allen Poe ("The Oval Portrait"). What is the relevance of these citations of other works of art within the film?