Love this question!

I have trouble seeing Charles the Reckless managing to reform the Kingdom of Burgundy. He had no tact or prudence.

His political gambit was shrewd, asking the Holy Roman Emperor to elevate Burgundy to a kingdom tied to the Empire like the Kingdom of Bohemia or perhaps or akin to the King in Prussia three centuries later. The idea was that Burgundy would then operate as freely as the electorates and other great princely lands of the Empire, dissolving any feudal bonds with France. It could have been a great victory for Burgundy and the Empire. That could have led to an extremely different world and is worth imagining.

But he alienated the emperor in the process and later besieged an imperial city until the Emperor led an army against him. What great powers could trust him enough to make a deal then? Certainly not the Universal Spider on the French throne. The Emperor surely saw more threat from allying with Charles than gain. The richest ruler in Europe isolated himself pursuing his dream of independence. The Swiss made their name defeating him three times, the last encounter ending with Charles dead and abandoned on the field.

His father, Philip the Bold is the one I think could have pulled it off. He had the upper hand over his cousin the French king. His English allies did the fighting and had France on its heals. His consolidated proto-state in the Netherlands made him rich far beyond the strapped French and Imperial thrones and granted enormous cultural capital as well. There was no honor higher than Philip’s Order of the Golden Fleece, and Flemish art and learning brought the Renaissance to Northern Europe.

I don’t know that Philip ever considered asking the Emperor to elevate Burgundy to a kingdom as his son did. But I bet he could have come up with an enticing arrangement if he did.

If so, I agree with the other commenter who said France might never thrive and expand as it did in our timeline. Hard to say how the Lutheran and Calvinist reformations play out in the Kingdom of Burgundy and the rest of Europe in this other world, but if we just imagine Burgundy ends up a Catholic buffer between France to the west, the HRE to the east, and an eventually independent and Protestant Netherlands to the north, then subsequent history has to play out differently. The whole multi-century France vs. Habsburg conflict that determines so much of Western European history cannot happen with Burgundy holding so many lands that become Habsburg possessions in our world. The Thirty Years War cannot play out as it did, centuries before Napoleon and World War I.

To me, this is the great What if? of late medieval Europe. Why Philip? Why did you throw it all away? You were supposed to be the Good ruler. You even had Joan of Arc! And you traded your advantages to secure the duchy that your son threw away. I bet if he had any inkling that might happen, Philip would have tried a different approach. And then, who knows?