If they had set up shop further north, like around Savannah and Tybee Island (which is actually towards the north end of the Guale Missionary province, but effectively uncontrolled) they might last a while, since that's a bit of a trip just to kill a bunch of heretics.
Yes, but to attack a bunch of pirates it's worth it. A major motive for the earliest French settlements in the American southeast was piracy, aimed at the Spanish for the vast amounts of gold they were exporting. Obviously, this attitude is going to put them into trouble no matter what-the fact that the French settlers were Protestants is just an excuse for the Spanish to be extra brutal.
In order for the early French colonies to succeed, a lot of things have to go right for them. They must be able to defend themselves against other Europeans: The Spanish, of course, but the English (who IOTL were helpful to the early settlements) could also be a problem. The colony must not starve, and simultaneously it must not piss off the local Native Americans by stealing food. Finally, there must be some economic incentive to get settlers to come-fur, tobacco, or sugarcane could work.
If the French manage to create a colony that survives, it's numbers could be fed by the wars of religion-Huguenots might decide to try their luck in the new world rather than fight endless wars in France. The Huguenot colony could remain loyal to the king as, overseas, they'd have de facto freedom of worship but a need to be protected from the Spanish and English. The crown of France could see the economic benefits of the colonies, and so keep protecting them. Though it may also decide to create some more 'reliable' Catholic colonies to counterbalance Protestant influence in the New World, and so do more to encourage immigration to the colonies-thus creating a populous French colony in the southeast.