Why the historical alterations?

*spoiler alert*

Luc Jardie was also based on Jean Moulin, a high-profile member of the Resistance. His death - that he died under torture revealing only one name: his own - is based on the fate of Jean Moulin. So evidently they mixed together different aspects of different characters to make a better movie.

Another historical alteration was having the Germans march around the Arc de Triomphe at the beginning, instead of through it, as they did in the Forties. I imagine that the French would not allow such a reenactment.

Well, I have a thematic answer for you. Melville would want to have the head of the Resistance a philosopher, and would want to take the time to show us the titles of his books, because this highlights the philosophical underpinning of the film, which was largely a kind of austere existentialism, a rational fatalism mixed with calculated decision-making that brings life-or-death repercussions. In this sense, the film is about more than the French Resistance (Melville went so far as to say it is not even a film about the Resistance!); it is a heightened allegory for the ethical decisions and search to maintain authenticity in life in general.

But Cavaillès WAS a philosopher/mathematician, so there is no real dissonance here. Local Hero's comments are excellent, though. They succinctly sum up the film's theme.