Peasantry is a class, part of the caste system of the time. A peasant could be a fantastic warrior, a poet, a wonderful singer- but he's not of noble blood, hence lowborn. Many years before this battle, the Anglos had recognized the power of the longbow, and the King (idr which) mandated that all males in the lands he ruled spent at least a certain amount of time practicing the longbow every day. So when King Henry invaded France, he called up his militias- and they were highly specialized ranged fighters. Usually levied troops throughout history weren't subjected to mandatory spear training or whatever, so they tended to not perform as well as the professional soldiers. We can also see this with the Beliaric slingers, from a small island in Greece- there was a tiny tribe that used slings to herd their livestock, so they were extremely proficient at it. Eventually outside forces enlisted them as mercenaries, and these guys were crazy deadly ranged specialists. It's remarkable how similar it was to the situation with English longbowmen, and it makes me wonder if Henry and his court were familiar with such peasant-training practices.