The question is simple, basically France is capable of acquiring the whole of the Burgundian Inheritance, either via Mary of Burgundy being born later and being wed to Charles VIII of France or the French having success in conquering it fully from the Austrians or maybe Charles the Bold is infertile after a accident and when he dies, Louis XI claims his lands and brings them in. Either way, the Burgundian Inheritance ends up fully French.
I was under the impression that “Burgundian Inheritance” consisted of two distinct parts: (a) territories which belonged to the French crown and would legally return to France when the male line of the dukes will extinct and (b) the territories acquired by the Dukes outside France which could legally be united with France by marriage but actually were the part of the HRE so if Charles dies without an issue Louis does not have a legal claim to them and, short of the marriage scenario, it is not quite clear how else he or his successors could get them: the French military system of that time hardly was adequate for such a conquest.
So marriage looks like the most plausible scenario to me but even it is not going to be peaceful: in OTL Max, IIRC, had to deal with the rebellious cities. Probably they would be as reluctant to give their “liberties” to a Valois as they were to Hapsburg.
Question is, what now? For centuries the ambitions of French kings lay in expanding towards the Low Countries well until Louis XIV and it laid the path for several wars that while not always winning, did manage to solidify the modern borders France has today alongside a centralized existence, so would the French kings turn to Italy now?
Even the inheritance by marriage scenario puts the happy beneficiary into a touchy situation with the HRE. Would a king of France accept the fact that he (as count and duke of this and that) is a vassal of the Emperor? Would the Emperor try to press this issue? Admittedly, without the Netherlands as a source of income the Hapsburgs are in a much worse position but still Max probably could rally the adequate resources to make the French life interesting.
The marriage scenario means that Max marries Anne of Brittany and the kings of France are getting a potentially “interesting” pain the their butt which they have to address before going anywhere. Well, and while Charles is a vassal of Max, Max is a vassal of Charles so how this situation is going to be reconciled? 😉
Then goes the obvious question of the next generation: Charles marries Mary and Phillip of Austria is not born (is there any male heir?). Max marries Anne and what is a byproduct? The whole OTL Hapsburg monstrosity may not come to existence and this will have serious geopolitical consequences specifics of which depend upon the details of your schema.
As far as Italy is concerned, if the whole circus starts (which requires Charles having settlement with the HRE ), then France still loses Naples - this was a strictly Spanish affair. But who is ruling the HRE and what are his resources? In OTL it took the unified Spanish-HRE resources to eventually beat France. So you probably need to have a similar situation (who is going to produce whom, etc.). Taken alone neither Spain nor the HRE would not (IMO) convincingly defeat France in the Northern Italy: Spain is lacking obvious reason and the Hapsburg without the Netherlands and then Americas does not have money.
So France, short of non-zero probability that its kings will manage to screw things up (as in the Naples), may quite well end up having Milan and Genoa.
Or maybe try and get the "natural" borders into the Rhine? This also ties into centralization as the Kings of France would definitely add those lands to the Royal Inheritance but the locals already didn't enjoy Charles' centralization efforts and they would like even less the French king ones, not to mention the reactions of their neighbors: England is probably shitting itself, Spain would be even more hostile and I can't imagine the HRE being happy that several lands of the empire are now under French control just like that.
England was not a major military factor and Spain, which does not have any claim to the Netherlands and County of Burgundy, after kicking the French out of Naples may not have a serious reason for the further expansion in Italy. Plus, without the Netherlands, even American gold and silver
may not be enough for the needed military effort (honestly, I don’t have a breakdown on that so this is just a guess based upon the problems the Spaniards had with financing the war with the Netherlands).
HRE is a tricky issue but it looks like that the Spanish and Netherlands’ money had been critical for financing a major war: the landsknechts had to be paid and the Austrian Hapsburgs tended to have empty pockets. So the French may get lucky.
