French crossbowmen were completely outclassed by the English archers, who could send deadly volleys farther and more frequently
The crossbow had a significantly greater range. While the longbow's potential rate of fire provided a vast advantage, the difference was the archer. Without the strength and skill of years of experience, the longbow would have provided little advantage. It was the warriors, not the weapon.
An Urban Legend perhaps, but I understand that the Brit's two-finger "up yours" gesture arose from the fact that the Frecnch cut those two fingers off of any longbowman they captured so he was henceforth useless. The "up yours" defiance indicated they could still use the longbow.