A friend of mine and I are having an absolutely uninformed conversation about the French Revolution, and it brought up a couple questions.
First, did the immediate horror of the Revolution spawn any "popular" conservative movements? I see on wiki that a boardly monarchist right wing formed in the French Parliament during the Revolution, but I'm interested in the effects amongst the public-at-large, especially after the rise and fall of Napoleon.
Second, and generally, what is the broader picture of the popular right? It seems to me as though "conservatives" have traditionally supported the upper-class and existing institutions. While we certainly (in the US, anyway) still see that lineage, when did the right become the kind of politics that could be held by salt-of-the-earth types? When did conservatism become popular among the lower- and middle-classes?
During the French Revolution, there was a strong Royalist current in the countryside that was eventually put down as a result of continued military pressure. The Vendee is best known of the revolts for being a bloody affair where future Marshal Augereau was involved. (A side note, Marshal Brune was murdered and ripped to shreds in Avignon as a result of Napoleon's defeat at Waterloo, the locals confused him with Augereau and he suffered a terrible death despite never being a part of the Vendee repression).
After the fall of Robespierre, there was a conservative shift in the French government where many of Robespierre's closest associates were executed and many Jacobin's arrested and tried, only to be pardoned later on. Napoleon as well was a part of these people as he was connected to Augustin Robespierre, but was pardoned for treason.
During the rise of Napoleon, there isn't as much of a pro-monarchist movement in France as Napoleon was Emperor. Areas with Royalist sympathies would have problems in recruiting or providing men for conscription but would never have a wide spread 'popular Royalist' movement as you are looking for.
After Napoleon, the Bourbons wanted to turn back the clock. Louis XVIII had been counting the days of his rule since the death of Louis XVI, so he had little or no interest in keeping the Revolution around after he returned to power.
To answer your second question, it is not as clear cut as how you suppose. I use the phrase Royalist as they would embody the "conservative" ideology since they wanted the Ancien Regime over the Revolutionary government. I cannot say with certainty that they saw the Revolutionary government as illegitimate but there was also a religious portion to it. The Revolutionary Government had changed a lot of the rules concerning the clergy, having the government replace bishops and have them swear allegiance to the government over the Pope, causing many priests to leave; with this, the common-people would have a hard time accepting the changes that were coming from Paris.
Overall, there were Royalist movements but they were usually crushed in time or turned into moderating movements against the Jacobins.