As people have already said in this thread, Joan d'Arc serves perfectly as a symbol of French liberty over foreign domination, as well as a symbol of France as a Catholic nation (which is something a Bourbon monarchy would like to emphasize), and her humble origins and rise the greatness. "Joan leading the defense of Paris in the Great War" would be a great propaganda piece. And there is that great staue of her outside the Palce des Pyramides. She also existed, so thats gotta count for something.
This is something I was thinking about, about a possible Bourbon-Orleanist restoration in 1871 in France. Marriane really became symbolic during the Third Republic but before that nations had been personified as a fair lady: America had Columbia, Britain had Britannia and Bavaria had, well, Bavaria - And there had been some male personifications too: John Bull, Uncle Sam (And a Johny and Billy during the Civil War), Deutscher Michel, Zé Povinho, El Roto and Srulik; so I wonder if down the line, lacking Marianne, a male personification would have emerged. Something like Poilu (or "Adrian" like the helmet), always next to Joan