Here's a bash of an idea, tear it to pieces if need be. The English longbow armies were made possible by a popular trend of longbow archery in England for about 150 years. When the trend ended the longbow armies became harder to raise, and thus when guns came onto the scene the great longbow armies weren't around to defeat them in rate of fire battles. Keep in mind too that the longbow has been around forever, it's just that its use was confined to professional hunters and other limited groups, it was it's widespread use that made the English armies possible.
Longbow use becomes popular in Anglo-Saxon England during the 900s, so much so that the ceorl portion of the fyrd becomes predominantly longbow archers. At Hastings the Anglo-Saxon archers decimate the Norman armoured knights (a-la Crecy), and the huskarls advance on foot to finish the slaughter, a decisive victory for the AS army. The AS then invades and takes Normandy and consistently wins border skirmishes with the French mounted knights. French knights become aquainted with mounted bowmen during the 1st crusade and decide that this is a way to match the power of the AS longbow armies. Thus the nobility of NW Fance add composite archery to the list of military skills they learn from childhood, altering elite opinion of the bow as a weapon.
By about 1100 the popular trend of longbow archery is on the wane in England, but horse archery is entrenched in the French nobility and not wanting to be left behind all of Europes nobility adds this skill to their arsenal. peasent armed with pikes and crossbows don't stand a chance against the rapid movement and firepower of horse archers. A new invention, the firearm, is tried on and off against the mounted archer/lancer, but after firing their first volley the horsemen fire 5 or 6 arrows before the gunners can fire again, thinning out their ranks in preparation of a final shock charge. The embryonic firearm is discarded as inneffective against the range and rate of fire of the bow and further development concentrates on cannon to fire grapeshot at horsemen from fortifications.