Don't attempt to engage 1:1, since the computer is fairly smart about reinforcing and you'll find yourself outnumbered. you have 20 units they have 40) - try to find isolated units to hit and destroy. *IF their forces outnumber yours 2:1 (ex. Make sure you hit them with all your forces and not have them hit your units one-by-one. you have 40 units, they have 20) - chase their army around and try to have an engagement on a territory with as little defense as possible.
*IF your forces outnumber theirs 2:1 (ex. (You would then move your split units back into the province once they engage.) Say if you each had 20 units in a stack, they most likely will not hit you, but if you moved 6 units away and only had 14 in the province, they'd move in to attack you thinking that they outnumber you greatly. A trick to lure their army is to split of part of yours so your defensive force looks weaker. They'll get up to -4 to combat rolls (-3 mountain, -1 river crossing) which is HUGE for combat. Try to force a defensive engagement around the area of Bearn (or the adjacent mountain provinces).
*IF* your forces are similar in number to them (ex. Well, since you have started the war already, a few tips for battles: