60 years in France.

[caravel]

This is a much better use for Army Champagne than if I allowed 600 of its men to be massacred in an auto-resolved assault upon the troops in the Lorraine citadel. They can be bribed later when I have some form of currency.

Chevauchée tactics are very worthwhile in this situation. But if you are to take the French provinces, you will face the same problems again. Once your economy is safe again you may want to start building catapults.

-Edit:

Won't razing Franconia and Bohemia and then leaving cause massive loyalist revolts though?

That's one of the risks. On the plus side it may give the French a lot of low quality (and hopefully low loyalty) troops that he has to support. On the other hand he might get a rebellion of FMAA and FK - but that's rare. There is also the possibility that such actions might trigger a civil war.

Personally I don't manually raze provinces as it's something the AI cannot do - which makes it a bit of an exploit IMHO.