The related chronicles of Monstrelet, Le Fèvre, and Waurin claim that the English took 1,500 or 1,600 French prisoners at Agincourt, but like most medieval chroniclers their large numbers are unreliable. The St. Albans Chronicle has what I consider the most reliable count: a bit over 700 prisoners, and the dead numbering three dukes, five counts, the constable of France, the seneschal of Hainault, the master of the crossbowmen of the king of France, almost a hundred other lords, and 3,069 knights and squires, a number so exact that it may be an actual count. Berry Herald counted the dead at 4,000 knights and squires and 500-600 "other men of war". The English count would have missed French dead dragged away in the night after the battle by local peasantry or stripped by them and thus unrecognizable as persons of rank. The disproportionate number of gentle dead is understandable when we remember that the other ranks had by all accounts moved to the rear of the formations before they came to hand strokes, and, less heavily burdened, would have had a better chance of getting away once the fight was lost.
That's a lot of prisoners and booty: roughly one prisoner for every man-at-arms in the English army, and the kit of two dead or captured French men-at-arms for every three fighting men in the English army, archers included.
Beyond the gear that those they killed or captured, what else would they have looted? Gesta Henrici Quinti reports that the French abandoned "their wagons and other baggage carts, many of these loaded with provisions and missiles, spears and bows." Conspicuously absent is any mention of the valuables that must have been in the French tents at the start of the battle.
Once it was clear that the day was theirs the English first concern would have been to secure their prisoners before advancing to the French camp behind the rearguard. There would have been time for servants to throw the most valuable items into saddlebags. The French would have abandoned the wagons so some of them could escape on the draft horses.
The English took more booty than they could bear away. King Henry ordered that the men could only keep armor sufficient for their bodies: the rest was to be heaped in a barn or house and the building burned. For the 3/4 of the army that marched on foot there must have been a painful struggle between greed and exhaustion.