Though argued stongly its debatable that the plate armour had evoloved from Crecy and Poiters in such that the process of hardening and tempering had become more understood, also that the quality of the arrow heads was variable ranging from cheap iron to proper forged steel. So the arrows themselves did little damage against the heavily armoured knights, and since the archers were more or less out of arrows by the time the first French battle had reached the lines the arguement about how much damage the bows did. The archers themselves being lightly armoured could move quickly in the mud and armed with heavy weapons; axes, maces, polearms could disrupt the heavily armoured knights in the flanks. Though knights were trained to wear armour so they could move easily in it, in thick mud falling over would have made it difficult to move, esp if people walked over you thinking you're dead, making an easy target for a quick dagger through the eye slot.10,000+ dead and hundreds captured? Slogging on foot in heavy armour through thick mud against 6,000 archers each of whom could shoot a minimum of 12 arrows a minute. 5 minutes in the killing zone, at least one quarter million arrows to negotiate. Beyond silly, borders on the Pythonesque. Sensible thing to have done would have been to pay them to go home.
they did have knights in the 3rd battle, but after seeing the destruction of the first two battles they weren't used. But if they were used in the first waves chances are that there would be more casualties as the horses would have died faster not being as heavily armoured and caused obsticles for the following troops.
Though the archers (mostly) were the ones that did the unchivalrous thing of killing the prisoners, this was due to an attack on the bagage lines with cavalry that were eventually driven off. If those knights had come and fought rather than gone looting the battle may have turned out alot different.
Plus with so many titles on the French side again their failing was theat they had no real commander but lots of little ones who didn't really work together.
Looking back yes the French would have saved themselves money if they let the English walk to the harbour. But at the time the English were seen as easy pickings. They were a small army outnumbered almost 2-1 if not more, they were tired, not well fed, most were illand possibly dehydrated due to diaherra and vomiting. (if you read Bernard Cornwall books, though not entirly accurate at the drawing of the battle lines, one of the commanders tells his archers they aren't allowed to go into the nearby forest but to "sh*t where they stand"). Plus their baggage trains were loaded with loot that they had plundered, so at the time the army looked like it would pose no challenge, just the French were mismanaged, that was the main downfall.