It's worth noting that--at least in the Skullgirls Digital Sketchbook and some other concept art--King Renoir is depicted as having his head missing, with nothing but a column of smoke coming from his neck.
Old plotlines state that he used a certain power to eliminate the Skullgirl-fied Queen Nancy that also cursed him to live headless. While that "power" seems to have been eliminated from the plotline, (it was related to the one that had Parasoul growing branches out of her covered eye, the "Black Tree", so you know it's quite old) it is entirely possible that Franz being a headless man is still the reason he's missing in the current plotline. Even if the origin of that status has been changed.
After all, it wouldn't make the Canopy Kingdom look very good to have a leader that's missing his head, would it?
In any case... Even if the headless plot has been entirely abandoned at this point, Parasoul is still definitely the one in charge of the country in King Renoir's absence.