Jean is not "involved" in the coup. There is/was no coup. Jean made those rumours go from branch to branch in order for this to happen. Now he is making allies, contacts, creating unrest and dividing the 5 chiefs, royals and eveyrone in order to throw down the system. Thus making a coup.
I get the feeling that Jean hates this "order" everyone talks about. His smoking is a sign of freedom and the only thing that gives away how he is against those rules and "order". I still think he is royal family somehow, maybe he is a descendant of a previous king, if there has been any change in the royal line or even from before the unification when there were countries.
Funny thing is that Grossular is actually loyal, a "patriot", to ACCA and its system and Jean is making it look like he is the bad one with a hidden agenda and trying to overthrow the system. Love it.