From The official website of The British Monarchy:
(Perhaps this story should be taken with a large dose of salt. Not only might it be self-aggrandizing English myth but, given their huge numeric superiority, it would have seemed foolish for the French to accept the offer.)
From what I’ve read, much ancient and medieval combat was about demonstrating personal prowess. Perhaps the battles OP asks about did occur but were historically insignificant because the parties just went to war again a year later.