Basic tactics would say that ANY force in a strong defensive formation, set up and staked out, would have an advantage, all things being equal. It only proves that the English were able to get the French to attack them more often, not that the English archers were especially invincible. They may well have been, but their success in fixed positions alone does not prove it.

The problem is that history is against your analysis as well, since there are only a handful of battles where the English shot up crossbowmen. Crecy, where the Genoese had left their pavises behind and got run over halfway by impatient knights, is the only notable example, and not a very good one at that. At other battles, such as Agincourt, the crossbowmen never got to fire at all. It was the English being on the defensive that gave them the advantage in those battles. The crossbowmen were thrown forward hastily to "prepare" the way for a cavalry or infantry attack with a few brief volleys of bolts, found themselves fighting an archery duel for which they were unprepared (having left their pavises behind), and run over or pushed aside by the "real" fighting men who wanted to get on with things. Things would have been more even if both sides had come intending to fight an archery duel. Yes, I know that crossbows fire slower than longbows, even with separate loaders. That's why you pay someone to carry a big wooden board in front of you or wear it on your back. It doesn't matter how fast the other guy can fire or how accurately (shoot really, you can only 'fire' a gun) if he only hits your shield. Unless you believe that bodkins pierce thick pavises too?

Actually, I wouldn't be surprised if longbowmen also used pavises too when facing enemy archers. In their case it would be held by someone else and raised to cover them when the enemy volley arrived (you can see it coming). The OP's issue was that pavise crossbowmen are protected against longbowmen but not vice versa, which is why longbows are at a disadvantage in archery duels. But making them more uber as a means of overcoming just one type of unit unbalances them against everyone else. Maybe the English need to bring Pavise Crossbowmen too to "tank" the hits while the rest of the longbows DPS. After all, the pavise in M2TW is not completely immune to arrow fire like it should have been IRL.