Transport all troops to Gascogne and get mil access from Navarra (Aragon too if you can). Leave a small 'bait' stack on Bearn, as soon as the French are about to attack (1 day before they arrive in the province) send all reinforcements to back up the bait stack.
Win because of mountains & river crossing penalty.
Protips: delete your heavy ships, they are too expensive and build 15 or so merc regiments. You want them as your bait to save you manpower!
Sound advice, in general. Few problems:
1) Bearn is not mountains anymore;
2) French leader is probably going to have better maneuver than you, negating the river penalty;
3) French AI seems better at avoiding battles in bad terrain and better about doing things that bleed manpwer.
That said, moving everything south IS your best bet, but engineering the necessary field battle(s) in terrain favorable to you isn't as easy as it was. You should still try this route. Bearn is hills and will still give you a modest bonus. But Navarra, Pirineo, Girona, or Dauphine will give you more. You'll need access to Navarra and/or Aragon and/or Savoy, but all three starts eating into your Dip slots (and you probably want to save some Brittany, for Scotland, for buttering up potential allies who didn't rival you at start). Dauphine seems the best place to try to suck them in, but is the most inconvenient for you to reinforce (with your mercs). Other people have had success luring them to Portugal and bleeding them there and along the way, but that means access through Castile, which can be problematic (as can Aragon, sometimes).
On the plus side, you have a lot more money for mercs and loans (for more mercs) and Portugal will join you. On the minus side, France can and will call new allies into the war. Once you merc up, time isn't on your side. In addition to their deeper manpower reserves, money, and new allies, BUR is going to attack, eventually. You may have to settle for a fight on close to even terrain. Given their general advantage, make sure you've got clear numerical advantage (again with the mercs)
Overall, is seems easier in some ways, but more expensive. I used to be able to do it without disbanding fleets or taking loans; I can't definitively say it's easier unless I can do that on a consistent basis, again. The tedious business of raiding, looting, trying to bleed their manpower seems more problematic (or I'm just doing it wrong in 1.8), so it seems to come down to one or two big, exciting battles; which is good/more fun, IMHO.
Caution, though. Vanquishing France, however you do it, is going to make for a duller ENG game, in many people's opinions. But if you win and decide to continue, a couple of changes in 1.8 make the PU a bit less attractive and more expensive. If your goal is to integrate them at some point, it might be cheaper (assuming you beat them) to just start the break-up process and take their provinces directly. If your plan is to keep them in a perpetual PU, the war can be a great deal, but you need to keep an eye on your relations, on their army size, and try to avoid liberation wars.
