Take the battle as it was, not some hypothetical "other field". That wouldn't be "Agincourt".
You have to have the mud. And the fragmented French command of rivals: almost still a civil war breaking out, which it later did, of course.
The English are Homogenous. That counts for a lot. That is probably the single most important difference that decides the battle.
But command isn't everything. The French army had their OB arranged and dispersed among the commanders many days before the battle. So everyone who had a command knew the game play. When the battle started, with, as noted above, the English archers attacking first, it was almost as if the French army went into "non player" mode, with every move prearranged, but carried off badly: about as badly as possible!
The flanking cavalry attacks were launched as per "the plan". But they were puny compared to "the plan's" hundreds on each flank: most of the men at arms had dismounted instead to take station with the first battle of dismounted men at arms. So of course, the cavalry attacks, being very undermanned, were overwhelmed by arrow shot.
It was not in the plan to have riderless horses crashing through their own infantry. Go figure.
The mud was not in the plan either. But it exhausted the French. They could hardly fight. But their formation was so dense that its momentum still nearly broke the thin English line. If you do nothing at all but play the arrow shot into the first battle, it can win sometimes; I'd say about a third to maybe half the time, the French first battle will win when it comes time to melee. When the French win the melee the battle is over but for the shouting: the second battle reinforces victory instead of defeat. And that makes all the difference.
Now, variants, with the same field, the same mud, the same command "structure", if we can grace the French with such!
If you allow a modification to "the plan", you can send all the French crossbow into the woods to flank the English line. Then while that duel is ongoing launch the infantry attack. Don't even bother with the cavalry; that is worse than a forlorn hope.
You can send all the cavalry, instead, to attack the English baggage, flank with the crossbow, and then launch the infantry attack. Try these. You'll see the English win a handful of times, if at all. That's my guesswork………