Sorry for the late response, something came up.
Fleche is not supposed to lose MP, although after checking both the state and the common event that grants the passive, I am not too sure why Fleche would have Leon's passive still. One thing that does come to mind as a possibility is that since passives don't actually disappear until the state is removed (There is a common event that checks to see if a passive is active at the start of every turn and applies the passive if the requirements are met) either by death or resting (In Leon's bed, not any others since Leon's bed does a full refresh that removes all negative and positive states), that could possibly be why Fleche is still be affected by it.
Short answer without deeper explanation: Not sure why Fleche is getting Leon's passive, but I suspect that Fleche never died or you never rested in Leon's bed. Try doing both of those and see if that works!