You're right : "inclure Chef Pierre est absolument nécessaire !" (Quite transparent French sentence, I hope!)
About the toque : it's almost a military hat in fact! The Chef is the Chief-Officer of the Kitchen Brigade - the cooking squad !-, in which exists a whole hierarchy. But it's true that now it is used also for the showing of. Victor loves to rule : perhaps that sometimes he reigns over his Chefs? Every domain deserves his attention. Do you think that then he wears a green and even bigger toque ?
One last thing about our strange French habits : the mustache is now really rare - or you must have a beard too and then you are a hipster. That doesn't seems the case for Pierre, but perhaps that his full name is Pierre Clouzot? He looks like a cousin of Peter Sellers...