“That's why Agincourt turned out that way.” I would not be so sure of this. Azincourt turned out this way because the French Nobility just ignored the Plan.

The 3 main example of the success of the Long Bow are Crecy, Poitiers and Azincourt. Each time the English Kings or Generals turned the geography at their advantage At Crecy, the top of the hill and the ditches that will break the French charge, in Poitiers top of the hills and natural obstacles, in Azincout the bottleneck configuration and the mud, all this combined with a rain of arrows.
The French re-conquest will be to deny this advantage (in building castles), and then turned the Long Bow required tactic against the English by the use of artillery.
To be efficient, the Archers have to be able to shoot a massive amount of arrows, and they need to be gathered. So they became vulnerable to the slow but long-range canons. If they spread or are unprepared, they become easy picking for the French Cavalry (as in the battle of Patay, and use of artillery for Formigny, Castillon)…