A Different Thirty Years' Intervention

What would be the consequences if France decided to help the Emperor in the Thirty Years' War. What would be the chances of a civil war caused by Huguenots, how would the war change, and how long after would it take France and the Habsburgs come into conflict with each other?
 
It would have to happen before 1624 because with Richelieu in power, France won't make any move remotely helpful to the Hapsburg. Raison d'Etat was kinda is thing. Even so, fighting against the Spanish and Austrian vise was kinda France's thing since François Ier. France allied herself to the Ottoman Empire. The Valois and the Bourbons did not feel fluffy inside when it came to helping Catholicism on the international stage.

But before 1624, the Hapsburg and Maximilian's Catholic League are winning handily without help. As for Huguenot uprising, there were a few, culminating in the 1628 siege of La Rochelle. Richelieu made sure that no one could pull that off again. Not particularly because of religious intolerance but because it had been a challenge to royal authority and thus had to be crushed. He went right back to financing the Protestant powers abroad.

The only way for Richelieu to help the Hapsburg is if Gustav II Adolf gains so much power in the Germanies that he destabilizes France's foreign policy aims (to wit, break the Emperor's control, keep the Germanies as fragmented as possible). And even for him to pull that off, it requires a Ring of Fire, if you know what I mean.
 
The actual POD I am thinking of would solve the problem of Richelieu by decreasing his influence by that point in history.
 
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