My basic understanding is that the French Resistance was united in its anti-fascism/anti-Nazism. Were communists, socialists and anarchist a large part of the movements or was it mainly dominated by those in favor of liberal democracy. Was there much conflict between the different groups?
Communists were a dominant part of the resistance. Their party structure was naturally designed to wage an underground resistance against the state, an example being underground party cells. And hence this naturally lent itself to resistance against the occupying Nazi forces.
They also had the ideological fortitude and inclination to fight against the occupying Fascists whereas a large segment of the French right collaborated with the occupiers. The pre-war slogan "better Hitler than Blum" was more than just rhetoric.
In reality, the French resistance consisted of an extremely part of the population, and hence why Communists, who were relatively few in number, were able to play such a large part in it. Post-war France lionized the role of the resistance, especially the Gaullists and portrayed a myth where "everyone was in the resistance", to salvage French national honor and to cover up just how much the average government bureaucrat collaborated with the Nazis. The role of the Communists were of course, marginalized to serve the purposes of post-war politics.
This is a pretty good lecture on the French resistance:
https://www.youtube.com/watch?v=H5NNaMiXQ-4&list=PLE653BF062C136B62&index=19