I do not have any official ruling however that event occurred in a recent game my group played. We ruled that once Vichy government fell all Vichy territory not occupied by Axis forces reverted to France. All moneys were collect into France while Paris was liberated. Then all territories reverted to Free French rules once Paris fell again. (UK collecting the money and FF forces conduct moves with UK)
The reasoning behind this is the initial establishment of Vichy resulted in extraordinary times. The German’s had just conducted the most successful military campaign in history. The French military was in a very difficult place. Once a government was established in Vichy an actual French government called upon its military forces to stand down. While Vichy was a German puppet it was still a French government. Once Vichy collapses it would never have risen again.