I suppose the men left who could handle those bows were the few, the proud, the marines. :-))
Probably the last hurrah of war archery in the western world was at Lepanto.
The archers here were the Ottomans using their composite bows, the eastern equivalent of the English longbow, probably with roughly equivalent draw weights and shooting distances.
The Catholic forces depended mostly on firearms for distance weapons, though there were no doubt quite a few crossbows around.
It is believed so many Turkish archers died at Lepanto that it essentially changed the balance of power in the Med. The Turks rebuilt their fleet in just a few years, but replacing tens of thousands of lifelong archers was not so easy.