What, all of the French? Or was it just the elected representatives voting on it? Do you happen to know the date of that vote or how many voted for and against?
I should assume, given the mention of "France" instead of "the French," that the intended term was to mean France-the-government, not French-the-people. And yes, what we today term the illegitimate government of Vichy France was indeed considered the legitimate and sole government of France in June 1940, duly empowered by the last electoral cycle to serve and represent the French people. Petain had been selected as Prime Minister due precisely to his intention to seek terms under, as far as I am aware, the constitutional powers duly vested in the National Assembly by the Constitution of the Third Republic, and contrasting with the lukewarm reception to de Gaulle in London, his ascension was regarded with significant popular support in the near term before the terms of the armistice were made clear and accepted. I'm a little curious, though. How many peaces were made by seeking a mass referendum of the entire population of the nation so vanquished? Does the absence of such make any peace automatically illegitimate? I'd see more of a point if you were talking about the subsequent vote for constitutional reform being put to popular referendum (this vote in the National Assembly occurred July 10, 569-80 with 18 abstentions, and was much more questionable under the laws of the Third Republic), or if you were contesting that it was a peace treaty on the grounds that it in fact technically was not a peace treaty at all (the June 22 surrender at Compiegne was only a temporary armistice, with a permanent peace settlement intended to follow after the end of the war), but quibbling based on the semantic definition of "France" as pertaining to a nation versus "France" as the summation of the French people seems an odd point to contest in this manner. (
EDIT) That is, I'm not certain how it's actually relevant. Conceptual agglomerations of people by culture and/or nationality don't sign peace treaties directly in most polities; their governments do.
At any rate, Vichy itself broke off relations with the UK after their sneak-attack at Mers-el-Kebir, only after which London recognized Free France as the sole government (though this was in truth already likely soon to come, given the aforementioned British attack on the French navy). The US, Canada, and USSR all recognized Vichy France as well, the USSR withdrawing this only after Vichy stated their support for the German invasion of the USSR in 1941 and the US and Canada both only withdrew their recognition when the Germans occupied Vichy France in its entirety, removing even the fig leaf of independence. On the very far end, various smaller states only withdrew recognition in 1944 with the resignation of Petain, while the Australians apparently went to pains to maintain diplomatic relations with both sides until the end of the war in 1945, in spite of being at war. I would probably suggest that 1942 would be the earliest point that, at least diplomatically, the Free French become the heirs to the French State abroad, though due to the contentious issue of its leadership in the eyes of the US, not necessarily a Free France under de Gaulle. De facto, I would suggest that the Free French do not actually become the French state until the actual liberation of France, for which I think Attalus has an excellent date right on the nose.
EDIT: Sorry, some clarity tweaks.