It depends. How much support for Occitanian nationalism is in southern France? As a free Occitania is, roughly, a Vichy France that doesnt consider itself France, the lack of a wide support would make it kind of unpopular or unfeasible. But anyway, if that were the case, there still could be a wide Occitanian revival in southern France just creating one or two alternate biographies, and the butterflies would not neccesarily wipe out WWII. OTOH, I can see Hitler doing that... why humilliating France when you can anihilate it?
But of course, that would have a wide effect in the African theatre (as there would be... concerns about the legitimity of the metropoli), and it possibly could put an end to the war before OTL, if the Occitanian Africa is lost in the earlier stages of the war. The effects would be very visible in the long term.
BTW, Occitania calling itseld Occitania or Catalonia makes a world of difference. Because if the puppet state calls itself Catalonia, the Spanish government would feel its interests directly attacked by Germany (think about the Greeks and the Macedonian issue, for example.) And when tide turns against the Axis, if the US asks Spain to declare the war on the Axis as in OTL, it could end up happening, with the effects that a Francoist Spain integrated from the beggining in the world stage would have.