I think that Vichy cannot attack a liberated Paris.
Rule 14.4.3 says that Vichy can only ever attack Free France.
The Vichy NRS says that “If Vichy attacks a Free French land zone containing units not from Free France, these non Free French units do not participate in the combat and are moved to the nearest land zone in their possession”.
However, the Free France NRS says that “If Free French liberates Paris, it becomes a Major Power (effectively becomes France again)”.
Plus, on a related Vichy question in the FAQ :
"Q: What happens if USA liberates Aquitaine? Does it become Free French? And if so, can Vichy attack?
A: Aquitaine is an original French land zone. Until Paris is liberated, “France” does not exist. Thus, USA can not give it back as per 9.20. So any Allied forces liberating a Territory in French Home Country gets to keep it until Paris is liberated and “France” once again becomes a Major Power.
Vichy cannot attack an US possessed land zone."
For these reasons, I would think that Vichy cannot attack a liberated Paris, as France has been reinstated as a major power and is no longer Free France. They would essentially get to wait until Southern France is liberated.