I recommend reading Simon Berthon's War Between the Allies about the conplicated relationship between Roosevelt, Churchill and De Gaulle.
Simply put, De Gaulle was reluctantly recognised as leader of Free France by Churchill since he was just a colonel with no political or military authority to represent a government-in-exile. Now, despite the Mers-El-Kebir incident, Britain kept open channels with Vichy during 1941 and also supported De Gaulle as a counterweight to Vichy collaboration with Nazi Germany. Churchill tried to work with De Gaulle during the rest of the war, but he also had conflicts with him based on the fact that he saw France's post-war interests and his personal standing in the Alliance more important then the Allied strategic goals. When De Gaulle once said that the French people saw him as a new Joan of Arc, Churchill replied that the British had to burn the last one.
The Americans did not broke off diplomatic relations with Vichy until May 1942. Why, do you ask, did the Allies still sought to drive Vichy France into the Allied camp? Vichy France was the legitimate government of France(as recognised by President Chirac in 1995), with no official bounds to Germany(no foreign troops on it's soil), so why not try to negotiate a change of sides with the legitimate government of France and negotiate with some fleeing officers, who could easily be clasiffied as traitors with no authority, not legitimized by anything until Germany fully occupied France in 1942(apart from slowly taking over the French colonial empire).
Roosevelt hated De Gaulle since he saw him for what he was: a conservative, nationalist, imperialist European, a man looking back to the 19th century and colonialism, which Roosevelt hated and already had to deal with them in Churchill. So Roosevelt tried to spite De Gaulle at every step: keeping relations with Vichy until the last moment, prompting General Henri Giraud against De Gaulle, proposing Allied occupation zones in France and UN mandate on Indochina, refusing to recognize De Gaulle as leader of Free France until after Liberation and refusing to admit De Gaulle at Yalta.