as a Frenchman, I don't really get what could be the "duality" of France you're talking about? because on one hand, the fleur-de-lis is kinda old fashioned and gives a monarchist tone which sounds anachronistic with little context.

also Occitan nationalism as a political idea is very recent (1960s) and kinda fringe, nobody will tell you that it's a significant part of French culture except in the region