Yes, but there’s a conflict on its legitimacy. The question is: had the National Assembly the power to pass the constitutional law of 1940 or not? For Vichy, of course yes, and then the Third Republic stopped there. But for the Free France (the political branch of the Résistance), this law was illegal, and then the Third Republic was still the legitimate form of the French government. That’s why in 1944, at the Liberation, De Gaulle didn’t proclaimed a new Republic, but passed an ordinance reestablishing the Third one.
It’s a difficult debate, complicated again in the case of the Free France that the institutions against Vichy always controlled a part of the French Empire.
However, my first comment was more because I understood the way you worded your first message as “the Nazis destroyed the Vichy regime” when the Vichy regime was established by the Nazis.