What I mean is, we know the Norman conquest of England changed the language, and other lasting occupations merged the indigenous peoples greatly affecting the original culture. Did the brief occupation of France have any affect at all?
Nothing along the lines of changing a language or merging French and German cultures but it did have a lasting impact in different ways.
First of all, the axis occupation and subsequent liberation lead to the rise of DeGaulle as president and leader of France. His legacy is manifold but to put it mildly he changed the political system of France by founding the Fifth Republic and leading the Algerian War, which in itself is as a lot of decolonization processes a result of the Second World War.
Secondly, the issue of Resistance and Collaboration left a rift in French society that had a long duree and continued for a very long time to affect French culture. Who resisted the Nazis and how and who collaborated was an issue that deeply affected and in some places split society.