Contmept is one of my favorite films, but having seen it only once, some time ago, I am not as "up to date" with it as you seem to be.
As I recall, the film is very complex and doesn't offer answers, instead posing questions directly for the viewer to decide. 
For me the film felt like an autobiographic exercise of Godard (much more than any other of his films i've seen), with the most significant thing in the film being the relationship of Paul and Bardot's character (sorry, I forgot her name). The focus being on Bardot, or on film, the two (woman and cinema) are - or aren't - on the same pedestal, for Paul. 

If i would do a paper I would focus more on the situation Godard found himself while making the film (his only "big-budget" international production), and his relationship to Anna Karina during this period in his life. 

What i also found very important for the film is the use of several different languages throughout it. 

On Lang, i would say he represents an "uncorruptable" person, the ideal director who can stay true to his vision whatever the circumstances may be. I think that's how most of the Nouvelle vague admirers of his works saw him. (see the book on him bardot is reading in the film). I don't think your description (later he made hollywood films) fits here, as what Godard is showing is a man who keeps his integrity (on one side Paul has Prokosch - the american, ignorant, rich and arrogant - on the other Lang - the european, with a vision, rich on tradition, and devoted to his art.)

For me this is one of the most honest films I have seen about relationships and representations, the way we perceive others and ourselves. Kind of what we put into the film (the image, the characters) will come back to us as a response. 

I think what you wrote above is a good starting point. Just keep to the things that interest you in the film, and speak to you. 


The final shot: 
you wrote: "Final shot: The camera moves slowly to focus its gaze on the sea, so that our gaze can finally rest upon its tranquil surface. Silencio
How about seeing the final shot as the shot Lang is composing in the film. Kind of an image in an image... Maybe only film (and ideal) can be the final "word" in a film. 

Whatever the case, it's obvious that I would need to see the film again to be able to offer you some significant help. 

Another point that came up just now. I think Bardot's position is less complicated than Paul's. At the beginning she loves him, later when she starts thinking more about his love for her, she loses the feeling and replaces (?) it with the title's Contempt. Has Paul actually ever "loved" Bardot's character? Or is she (like karina for Godard) a woman to project his obsessions into. An object more than an individual subject? Which gaze can make an object of a person, and how is the "cinematic" gaze of the camera related to this. How do you give yourself, and how do you take away from another - what is reality, honesty on film, and what manipulation and possession?