This is a somewhat complicated question as there were a number of different people who could be called the leader of France during the war.
When the war began, the leader of France was Edouard Daladier. He was the prime minister when war broke out in 1939. Of course, France was defeated rather quickly in the war. When this happened, part of France was occupied by Germany but the other part, known as Vichy France, retained nominal independence. The leader of Vichy France for as long as this entity existed was Philippe Petain. At the same time, however, Charles de Gaulle was seen as the leader of the Free French in exile.
All three of these men, then, could be called the leader of France during WWII.
Charles de Gaulle