If he reaches this extent, the Bold could just try to steal Provence and crown himself King of Burgundy by having all of the Kingdom of Arles
This was actually kind of the plan in OTL. He wanted his daughter to marry the Duke of Provence (or maybe it was the Duke's son, I'm not 100% sure). Problem was that Emperor Maximillian would definitely refuse to support Charles's claims unless Charles betrothed his daughter Maximillian's son.
Charles the Bold is probably the best ruler for a period of aggressive expansion, while his heirs (Margaret if she lives longer, any male heirs he might have had) would have to maintain peace and deal with the consequences of their father's audacity. Savoy extends the borders too much, though it lies in the historic Burgundian/Arelat region so maybe keeping it might lend some credence to Charles's claim to the Kingdom. Perhaps if he gives up any ambitions north of Franch-Comte then maybe he might gain more in the south? So no lordship over Cleves, Frisia, maybe content himself with leaving the bishoprics alone...
I think that he should try to trade the outlying territories to gain a contiguous territory. In the Netherlands, I'd suggest happily trading away everything north of the IJssel. Frisa, Groningen, the Oversticht section of the prince-Bishopric of Utrecht (which could be compensated with additional authority elsewhere tithin Burgundy, I'm sure-- especially if Maximillian is backing the plan) and Zutphen. Whatever (varying) power Charles has over those can and should be traded for control of more valuable (to him!) lands that can increase the contiguity of his kingdom. He ought likewise to give up Mark, and ideally, he could try to split Cleves, keeping just enough to connect the Veluwe and Guelders handily, but giving up the rest.
Further south, he could sacrifice some outlying parts of non-contiguous Lorraine, as well as the Breisgau, Basel and other minor outlying holdings in Switzerland. The idea would be to trade everything mentioned up to this point with those who are holding certain lands that threaten Burgundy's territorial contiguity.
On the French side, everything south and west of Artois should be given up, as well as Ducal lands of Burgundy (yes, I mean it) and Bar. The authority Charles has there should be traded to the French crown, in exchange for recognition and some lands in the south that would greatly improve Burgundy's contiguity there. This would be a major win for France (direct control over coveted lands gained without a single battle!) but would likewise get Charles far greater security in exchange for lands he couldn't really hope to defend anyway.
The result would look something like this (with sincere apologies to the cartographer for my crude lines):
Still not what you'd call defensible, but far more contiguous, endowed with recognition from the neighbours, and made up of all the lands you'd
really want to own in this scenario.
You mentioned that the Kingdom would be within the HRE- does that mean that Duchy of Burgundy and any French areas (Flanders, Vermandois, Rethel, Macon/Charolais) would then fall outside of the Empire as "side territories" while the true base of power is in the Imperial areas? Or would that kingship mean that the Burgundian lands formerly under French vassalage now fall under HRE's domain?
The above scenario of 'claim swaps' would solve this problem for most areas in question. Only Flanders and Artois would remain as French lands (that happen to be in personal union with Burgundy). Depending on the exact circumstances, varying options would be available. If france is really weakened in the scenario, then an alliance of england, Burgundy and the HRE can probably force France to rescind any claims to Flanders and Artois. That would be the neatest solution. In that case, they would no doubt end up inside the HRE, along with the rest of the kingdom. If France retains greater strength, the existing situation would be perpetuated, the kingdom proper would fall within the HRE, and Flanders and Artois would remain outside the HRE.
If any other land swap (or even no land swap) occurs, we may assume that any French lands remain French (but in personal union with Burgundy), and outside the HRE.
In the unlikely event of a total France-screw, it's even possible that all French lands in personal union with Burgundy are split wholly from France, and handed over to Burgundy directly. I'm sure Charles secretly dreamed of that at night, but it's very improbable that it would happen. If it did, Maximilian would certainly demand that those lands are included into the HRE.
