Hmm while interesting it kind of derails the idea of an inheritance
I'll think about it though.
Not necessarily, it may lead to Burgundy keeping a larger slice of the pie. They may be able to keep more of the disputed areas, which could be inherited by the female line. The 'Burgundian vassal states' within France would be lost though.
The duchy of Burgundy actually is interesting too, when it was given to duke Robert the Old (founder of the Capetian house of Burgundy), younger brother of king Henry, in part to settle a succession, he and his descendants gained the right to pass it to all natural heirs (so women could inherit or pass inheritance in the absence of men).
When the last duke of Burgundy of the Capetian house of Burgundy (Philip of Rouvres) died , there were two claimants, king John the Good of France (by proximity of the blood) and king Charles II the Bad of Navarra (by primogeniture). France didn't like the thought of Burgundy passing to Navarra and moved quickly, but the Estates of Burgundy insisted that Burgundy was kept as a separate entity apart from the Lands of the French Crown (John may have originally intended that). Finally he gave the inheritance of the duchy to his youngest son and arguably favourite son Philip the Bold (his courageous behaviour also saved his father at the the battle of Poitiers). Philip in return had to renounce his previous appanage duchy of Touraine, this inheritance was later confirmed by (John's son and Philip's brother) Charles V of France.
France claimed Burgundy had become an appanage, whereas later Valois dukes of Burgundy and their Habsburg heirs disputed this. The outcome of the 1435 congress of Arras, which acquitted Burgundy from fealty and homage to the French king may have strengthened that view.
Still even with a weaker France and stronger Burgundy, I consider previously 'Burgudian vassal states and territories under Burgundian influence within France'* lost, and Burgundy would be fighting to keep as much as possible from their own dynastic lands within France. Those territories (I might forget a few lordships) directly held by their house were the duchy of Burgundy, the county of Flanders the county of Charolais and the county of Artois. I would rank those in the following manner: the duchy of Burgundy most likely becomes French (though they could retain the title); Flanders is the most likely candidate to stay Burgundian, followed by Charolais; and Artios would be somewhere in the middle. Burgundy might be able under these conditions to exchange Charolais for Artois (maybe without the enclave).
Without these (necessary for this scenario) changes (a weaker France and stronger Burgundy) I'll strongly advise to follow the established consensus in this thread.
(*= counties of Macon, Auxerre, Boulogne and Ponthieu, the county of Vermandois, Picardy (Somme towns) and the county of St. Pol (Burgundian sphere of influence))