Likely not. For several reasons.

One, a number of powerful nobles had embraced Calvinism. John Calvin himself believed that the reason the Huguenots were able to flourish was the conversions of nobles like Jeanne III of Navarre and Louis I, Prince of Condé.

Two, the French crown was in dire financial straits, which would have made it unlikely for them to support expeditions in the Americas (which often failed). The lack of funding itself was a major reason why the Wars of Religion kept reoccurring: the crown lacked the funds to either enforce the majority of its edicts of tolerance or destroy the Huguenots entirely. This was because the constant warfare Charles VIII, Louis XII, François I, and Henri II had waged against Italians and/or the Habsburgs had drained the treasury and the reoccurring civil wars disrupted agriculture, which just created something of a vicious cycle.

Third, religious tension in Great Britain wasn't actually eased all the much by having colonies. While some Puritans were fine going off to Massachusetts Bay Colony, there were plenty of them that weren't, like Oliver Cromwell, and that other issues led to the Wars of the Three Kingdoms.