France
War in the Midst of War
Both parties struggled to control the crown while at the same time attempting to out-maneuver one another. As often happens in these situations, rivalries of purely local significance soon became entangled in the larger one so that we find "Burgundians" and "Armagnacs" throughout France. But in any given town or county, this lord might be a Burgundian merely because his despised neighbor was an 
Armagnac, implying nothing at all about relative support for or against King Charles or the English alliance.
The rivalry therefore played out at multiple levels, rarely to the benefit of the French crown. The most notorious manifestation came in 1407 when Duke John of Burgundy (Philip's son) engineered the assassination of Louis of Orleans. This treacherous murder set off a vicious civil war that completely distracted France from the war effort.
Finally, the Armagnacs arranged negotiations in 1419 between John and King Charles. Because neither side trusted the other, the two men with their retainers met on a bridge in northern France. There the Armagnacs stabbed John to death and hurled his body into the river before the very eyes of the mad king, who scarcely understood what had happened.
This incident induced John's successor, Philip the Good, to throw in with the English. It was this Philip who helped the English dictate the infamous Treaty of Troyes in 1420.