Okay, having looked this up again (I hadn't for some time), I will have to back down from my position that the longbow killed plate armor. But the longbow did demonstrate that it was no longer the panacea it had been (as at Agincourt and other examples), and it gradually faded starting about then, through the advent of early firearms, and basically died in the form of full-body armor not long after.

The French men-at-arms reached the English line and actually pushed it back, with the longbowmen continuing to fire until they ran out of arrows and then dropping their bows and joining the melée (which lasted about three hours), implying that the French were able to walk through the fire of tens of thousands of arrows while taking comparatively few casualties. But the physical pounding even from non-penetrating arrows, combined with the slog in heavy armour through the mud, the heat and lack of oxygen in plate armour with the visor down, and the crush of their numbers meant they could "scarcely lift their weapons" when they finally engaged the English line.

When the English archers, using hatchets, swords and other weapons, attacked the now disordered and fatigued French, the French could not cope with their unarmoured assailants (who were much less hindered by the mud). The exhausted French men-at-arms are described as having been knocked to the ground and then unable to get back up.