The French didn't really fight at the start. They (and England) watched Poland get invaded, then turned their backs on them and did nothing. This original Western betrayal followed by appeasement of Stalin by all allied powers is what really fucked over Eastern Europe, so thanks for all my family that got raped then murdered!
Then they sat around and continued to do nothing until they were invaded, and lost the war within 5 days of it starting and were immediately ready to capitulate. Even Poland lasted much, much longer against Germany and the USSR attacking both sides, with no help from anyone at all. A legendary military failure, and one of the main reasons French military accomplishments are ignored in lieu of calling them cowards.
The Free French Forces were successful, but keep in mind that America had everything to do with Lend-Lease, logistics, and operations to liberate French colonies starting in 1942 that weakened Vichy France and gave de Gaule the momentum to build up his army and participate in the invasion of Normandy. Another American operation I must add.
As far as military casualties are concerned, I would say about 150,000 French died fighting Germany, and 50,000 (probably less) died fighting the Allies, mostly defending Vichy France colonies. By the way, France had 200,000 military deaths in WW2, America had 400,000.
And 100,000 French Jews were forced out of their homes and sent to die in all the wonderful ways of the Holocaust, with full enthusiastic collaboration of the French government. One of the reasons I find France in WW2 so distasteful, they gleefully helped to carried out the Holocaust, killing 1/4 of all Jews in France.