If Charles the Bold doesnt die heirless, Austria never inherits Burgundy, and Burgundy therefore manages to hold on to all Benelux, Burgundy proper, Franche-Compté, and to have a land bridge between it all, lets say it also manages to get Lorthighen.
So basically, youd have a pretty solid country covering north-eastern france, luxemburg, belgium and the netherlands. Working from there is pretty easy. Obviously, that country would always have to be wary of wars, as it would stand as a buffer between hostile France and a lukewarm HRE.
It would need at the same time to develop the trade and naval traits that made Netherlands successful in OTL. Its logical ally would probably be England. Spain's decline in TTL would be slower, without all the troubles brought by a rebellious netherlands.
Starting earlier than Netherlands in OTL, and later incorportating alot of portugeuse colonies as in OTL, Burgundy could build a pretty strong empire. The peak of the Empire would be the 18th century, when England owns Hannover (thus securing Burgundy's eastern border). Before that, obviously, there would be huge changes, like, no Westphalia, and probably no Germano-French wars, unless Burgundy picks a side.
Nontheless, Burgundy was traditionally lukewarm to the HRE (Though she was a member), so other conflicts would probably still bring about the decline of whatever central authority exists in Germany throuought the Renaissance.
As for modern times, lets say Burgundy survives and consolidate until the era of revolutions. There, it begins a slow colonial and commercial decline. The French revolution can still happen, though it could as well not, but lets say it does. The victorious armies of France allows the realisation of an old french imperial dream; fusion with Burgundy, to break England's might on the continent. However, later misfortunes in the war push back France to its pre-war boundaries.
Burgundy is reborn, though changed forever by the French civil laws and a newfound desire for the ideals of the french revolution. Though its colonial empire is largely lost, Burgundy industrialize very fast, just one step behind England, propelling it to world class power. When, later this century, Prussians brings war to Burgundy, this industrial might fails to translate adequately on the battlefield however, and a behemoth united Germany appears on Burgundy's border. Worse: the punishment for refusing to join this german union, for Burgundy, is a serious loss of territory in the north and the east. The German Kaiser is crowned in the High Palace at Aix-la-Chapelle.
This humiliation brings Burgundy much closer to France. Thirty years later, they get their revenge after a long bloody war that leaves Europe in ruins. France, Burgondy, England and the Ottoman Empire finally defeats Germany, Austria and Russia. Vengeful Burgundy now extends to the Rhine.