I'm going to copy/paste from an older comment I made on the subject a while back.

Plenty of other countries did recognize the effectiveness of English longbow archers, but it was far easier to simply hire a band of mercenary English bowmen than taking the time, expense, and effort to train groups of commoners in the use of the longbow. The Dukes of Burgundy frequently hired English longbowmen for their armies. In 1448, King Charles VII of France issued an ordinance declaring that some men were now required to train with bows on a regular basis for use in the king's army. In exchange, these men were to be exempted from royal taxes and some other privileges. Their effectiveness in the reign of Charles VII is debatable, but these units declined into complete uselessness under later kings.

The short answer is that the use of the longbow was deeply embedded into English society and culture in a way that was difficult to replicate. You couldn't just hand out bows to the local militia and tell them to get to it. While longbowmen were very useful to the English, they weren't so amazing that they revolutionized combat and made everyone shit their pants just by showing up. Outside of the French attempt at creating an English-style corps of archers, there wasn't any particular reason for every principality in Europe to suddenly abandon their usual military structure and begin training longbowmen.