Is there a specific type of legitimacy or context for which you are curious?

Otherwise I am afraid the answer is really; "Depends on who you asked."

Even amongst the French colonies there was a variety of positions; recognizing Vichy, recognizing Free France, or recognizing neither but supporting Free France. This is an issue that seems to come up here with some regularity so check [here] (http://www.reddit.com/r/AskHistorians/comments/32bzqk/in_ww_ii_why_didnt_french_north_africa_surrender/) to see some more specifics about why some colonies declared for Vichy and some for Free France.

Both and neither depending on your perspective. Vichy France was puppet state controlling southern France, but organized under Fascist ideology. They were dominated by Germany, but retained some powers for internal policing etc. The Free French army led by De Gaul was a large organised resistance based mostly out of England, and consisted of mostly French citizens (or people from their colonies) who wanted to fight the Germans. Not to be confused with the French underground. Free French troops fought as military formations equipped by the Americans and British, and De Gaul would become the next President of France after the war.