Burgundy tried to cut ties with France a few times. Charles the Rash (you can see where this is going) tried to sever Burgundy from the France and ended up embroiled in a conflict against the Swiss and Louis XI as part of the League of Public Weal. Between 1473 and 1477, these two factions fought and Charles met his fairly grisly end at the Battle of Nancy in January, 1477.

This lead to a succession crisis since Charles' only direct heir was a woman (Mary) and the question of whether or not Burgundy was a fief--which she could inherit--or a appanage, which she could not under Salic law. Appanages are interesting in their own right, but the abbreviated version is that they were land granted by the crown and therefore subject to the same rules of inheritance: since you could obviously never have a woman as the direct heir to the throne, you could obviously never have a woman inherent Burgundy. This was an open question since the idea was somewhat new. Before the Hundred Years' War, women (or at least a woman, Mahaut of Artois) inhereted appanages.

Louis' case was actually pretty weak. The 1363 charter uniting Burgundy to the crown explicitly stated that the king's claim to Burgundy was not through his pejorative prerogative powers. The Peace of Arras (1482) reflects this somewhat conflicted stance, reuniting Burgundy to France but assigning parts of the disputed territory to the dowry of Margaret of Austria, who was to marry Charles VIII.

I'm running very late at this point and need to get home, but that marriage never took place, so the dowry was never realized, leading to yet another fight over the relationship between France and Burgundy, in which France ceded the Free County of Burgundy, but not the Duchy of Burgundy.