I'll check out Cornwell's book. It was quite a battle, as you know better than I. The British were hugely outnumbered--5000 against 30,000-100,000, and won mostly because of their superb archery.
There's an excellent 1989 movie of the Shakespeare play, directed by Kenneth Branagh, who also plays Henry. The rousing speech Henry gives his troops before the battle is used by actors as a show-off piece.