For some strange reason, monarchism has always been somewhat common in France. The problem for the monarchists - and this is a problem for monarchies everywhere - is that everybody likes the of having a king so long as they're the king. Hence the three major factions.
True. There hasn’t been a legitimate succession to the French throne since @1824, so the question of who is the legitimate heir is rather confused.
Still, this is something that the French have several times worked out in assembly in other past cases.
No, that is not the case at all. I am as commoner as anyone can get, -- I barely know my grandparents, -- but I am a monarchist, and yes, I will prefer most any king to most any democratic 4-year-lease government any time.