Indeed but i don't think Louis would want to destroy the Burgundians like the armagnacs. The man was behind 3 peace treaties. It was 3 fragile, bad peaces but it shows what he desired most. An end to the civil war. With this spirit AND the muscles he could acquire, he can force John the Fearless to negociate, who knows that he doesn't have a fanatical enemy before him. And this time, peace would be more solid. And one more thing, princes can make peace but the king and his heir have a far more precious power: they can forgive. Officially, no one can fight that. If Louis forgives John, it's not a peace treaty, it shows that Louis is superior to John. The Armagnacs could grunt but they would have to bend and John would prefer that to a fragile peace.
Hmm very interesting, would certainly make for an interesting set up