The vast majority of the French are so obsessed with their republic (liberty, equality, stupidity) that the chances of a French monarch reemerging are slim to none.
There are probably more serious monarchists in France than in any other Western European country. You don't know what you're talking about.
OP, for more information about groups, look up "French Legitimists." There are many groups of Legitimists. Many, too, are orléanistes, supporters of the House of Orléans and its claims. These people are rarely devout Catholics and tend to be liberals. Action Française is one of the most famous orléaniste groups.