An English Princess for a French Prince, Question?

So, this is something I've been wondering as of late, during the reign of George I/ George II I believe there was a plan to marry Anne, Princess Royal to Louis XV, now the plan failed because the French wanted Anne to convert to Catholicism. This has gotten me thinking, what would be needed for a successful marriage between an English Princess and a French Prince at around this time? A different dynasty on the throne? Different political circumstances? And if the marriage did go through, what might the consequences of it be? Especially in the scenario where there is no Act of Settlement, and potentially no Bill of Rights?
 
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