Taking on the Blue Blob, eh? I'd recommend leading their doomstacks into low supply provinces that you have managed to scorch, so that they get done in by attrition. You might also try distracting their armies as you sneak one of your own onto their capital, then use spies to speed up the siege. If you can get a seperate peace with their allies, take Paris and a province you want to take, then you could probably get away with a peace deal including that province. Burgundy has pretty good generals, as far as I remember.
What really matters, though, is driving their war exhaustion up. Do this with attrition, by winning battles (pick them carefully) and occupying their provinces. Any war against France is going to be one of cunning manoeuvres, so I wish you luck in this rather challenging task.