France was not completely overrun during the original blitzkrieg. Her armies were battered and the country was on its knees, but she still had resources. Like Belgium and Holland, she had overseas colonies to draw on. Unlike them, she also had a significant naval fleet. France's resources were significantly greater than those of other governments in exile, but she had one great problem that they did not face. Before the country was overrun, she formally surrendered. Her government made no attempt to escape and continue the fight from abroad.
The actual purpose of any government is to perpetuate itself. Its stated purposes of leading the people, improving the economy, etc., are important only insofar as they contribute to the survival of the government. This is not often presented in such stark relief as it was in France during WW II. The French government surrendered. The French people did not. The people were, of course, overwhelmed by events, but their actions during the war showed that no greater percentage of them gave up hope than happened in any other occupied country. The fact that their government did give up however, led to great confusion within the country and great distrust among the 'allies'.
I see two reasons that the Allies were not particularly helpful to the Free French government led by DeGaulle. One was simple suspicion. Since the recognized government had surrendered, and in fact joined with the Germans in an effort to maintain a misguided 'honor', how could they trust DeGaulle and his people? At worst, he might be an agent from the foreign camp, at best he was a 'traitor' to his own recognized government.
