Massed Longbow fire was extremely effective, to the point that the French started using it themselves, but over time there was a tendency to skimp on the more expensive men-at-arms, sergeants and even knights. Longbowmen backed by sufficient cavalry and infantry would be devastating but without proper support they would be required to fight hand to hand themselves, and every archer swinging a poleaxe is an archer to raining death upon his enemies.

Combined arms will always beat a one-note army and it was the failure of the English generals, and their inferior economic position at the time, that cost England the Hundred Years War in the end. Had Henry lived another ten years he would have been able to claim his right as King of France, if he could maintain control over enough of the coast he could have likely taken and held all of Normandy and Brittany and Henry VI would have had a better general position when he took the thrown.

Bear in mind, Henry V's death also sparked a succession crisis in England, and that's what really ended the Hundred Years War.