Intermission
Before the epilogue is written I wanted to share my thoughts on the seemingly only way to defeat France with Burgundy in EU3 2.1. I am sure there are military geniuses out there who will disagree with the "only" part. I would love to be educated and proved wrong. For now, however, this is the only way I know.
1) It is pointless to fight to gain white peace. France is there to stay and France will attack you sooner or later, again and again. Unless it is beaten and/or weakened France cannot co-exist peacefully with Burgundy. Thus, when the war starts your goal should be victory and not a draw or minor defeat. Having said that, I already lost two wars to France, ceding territory each time, so apply my advise with care
2) Like any superpower in EU3 France will never agree to peace unless you annihilate all of her armies, exhaust her manpower supply and occupy most of her territories (all preferrable, but not always doable due to high revolt risk and manpower problems you are sure to experience yourself by the end of the war).
3) Defeating France's armies is hard. They seem to have excellent leaders and manpower supply comparable to Soviet Union's during WW2. Still, it has to be done. In my experience (after four wars fought with this hydra of a country), offensive operations early in the war are doomed to failure. Every time I go on offensive too soon I am able to score couple of victories, capture couple of provinces and then lose badly to waves of French cavalry and infantry. Remember also that this is Magna Mundi, which restricts player's cavalry regiments (unless you want to bankrupt yourself by paying those punishing extra fees). Where am I going with this? Saving your armies is your top priority.
4) Can you hope to defeat an enemy by staying on defensive? No matter how hard I've tried, the only sound (soundly crazy is more like it) strategy I could come up with is to let France capture 5-6 provinces first. You shouldn't let them go without a fight, but fight only when you are sure to defeat the enemy, retreating even from evenly matched battles. Once those provinces are lost France will try to spread her forces around them first, waiting for garrisons to be restored. Eventually, French will try to push further, but still trying to protect their conquests. At this time, with an army of no less than 10,000 men you should start attacking France's weakened armies (attrition works, even if seemingly slow), once again avoiding larger armies at first. At this point your main objective is not to win the battle, but to inflict heavy casualties on the enemy without losing many men yourself.
5) No matter how weak they are later in the game, mercenaries you will need sooner or later. Accept this fact, but use them with care.
6) Merge regiments before battles. By now your manpower is already low, a lot of regiments are weakened by years of fighting and it takes forever to restore them to their original strength. Merge similar regiments, even if it costs to build new ones later.
7) Economy. There is no way to win the war without minting some cash to support the increased army maintenance (mercs cost money and raising new regiments does too). Might as well start early on. Keep your eye on the inflation, but again, don't think you can get away with 0% inflation when fighting France.
8) 5-10 years later... So far we've used our main army to beat up smaller enemy armies. Our second (and maybe third: I prefer two large armies, but some may find it beneficial to use one large and two smaller armies), have liberated some provinces, avoiding the battle at all costs, of course. We begin to notice that larger French armies operating on our ground are beginning to lose more and more men to attrition and assaults. With little luck, we will be able to easily dispatch them now (remember, our land tradition is high now and better leadership is worth the money spent). At this point we can start re-taking multiple provinces with several 1,000-3,000 strong armies. Mercenaries will do, since we don't expect these armies to fight. Guard their progress with one of your larger forces, with others taking war to France, grabbing an occassional province and beating up French reinforcements.
9) If you have allies and vassals and they have not deserted yet do liberate them from French occupation (yes, they will be occupied, France does not take chances). They will be really useful fighting those rebels (yes, there will be a lot of rebels, especially if MM's Reformation events take place).
10) You will have to have tons of patience. If you are slow like me a war with France may last good 10-20 years. You will have to convince yourself that you enjoy this meatgrinder, otherwise frustration will force you to quit the game. Oh, and don't be greedy. No reason to wait extra five years, spending precious cash and manpower for that special four province peace. If the enemy offers two or three provinces, accept without hesitation. After all, you are guaranteed to have another war with France sooner rather than later.
I hope someone will find this useful, drop a couple of lines if you do. I do welcome constructive critique and will answer any questions regarding my sad performance as would-be France conqueror