There are account of piles of bodies in medieval sources, but some of them seem quite exaggerated. The author of the Gesta Henrici Quinti, an eyewitness to the Battle of Agincourt, said that "a great heap grew of the slain and of those lying crushed in between" in front of each of the three battles of the English army. However, the Gesta's author was a priest, not a soldier, and was therefore behind the lines when the battle was taking place. His account of bodies stacked "above a man's height" seems dubious at best, especially when he goes on to describe men climbing the giant corpse-wall and fighting on top of it. Were there bodies stacked like something out of a metal album cover? No, probably not. Were there less exaggerated piles of corpses at Agincourt? Most likely. Isolated knots of French soldiers, whose advance had been disordered by archery, disorganized commanders, and bad terrain, were ganged up on by English men-at-arms and archers wielding hand weapons. French accounts also provide evidence the existence of small piles of corpses. The Count of Richemont was found wounded under a couple of corpses, with his surcoat stained red from the blood of the slain. The English picked through the piles of bodies to find wounded prisoners to take for ransom and to strip armor and weapons that they could use. Any gear that they could not take with them was burned to deny it to the French.

We do know that some prisoners were taken off the field during the battle. That, along with other pieces of evidence, indicates that there were breaks during the Agincourt fighting as various waves of French soldiers attacked and were defeated. There wouldn't have been enough time to properly remove all corpses from the immediate line of battle, but wounded English soldiers, like the Duke of Gloucester, could be taken behind the front line along with important prisoners. There was at least enough time during the battle for the English to begin separating their huge number of prisoners. At least a few French soldiers were locked up in a nearby farmhouse, which was eventually set on fire.

I think this goes without saying, but this episode only aired yesterday. The question is fine, but if you are opening this thread, you should expect SPOILERS in the text. If you plan to watch the episode and have not yet, you might want to close this tab!