Would the thirteen colonies (future USA) have wanted to emancipate themselves from the UK if France had preserved its territories in North America?

For me, the thirteen colonies simply couldn't have broken free from the British. At the end of the Seven Years' War, the English demanded that France cede its territories in North America, thus eliminating the French threat which allowed the thirteen colonies to no longer be dependent on English protection against France. As long as the French threat was still present, the thirteen colonies absolutely needed British protection.
Would the thirteen colonies (future USA) have wanted to emancipate themselves from the UK if France had preserved its territories in North America?
Would the thirteen colonies (future USA) have wanted to emancipate themselves from the UK if France had preserved its territories in North America?
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