I'd probably have go with Henry V, only lived to be 35 having become ill on campaign and lost much of his territory but what an exciting career.
Display of courage and interesting character.
This is just my opinion, I'm not calling you out or anything, but Henry V was not just a brilliant leader, and warrior, but he was a first class administrator, and he did what no other other English king would do before or after him, and he got the French to put an English heir to their throne. That he never lived to see this was unfortunate, and part of the risks of warring in those days, i.e, risks of disease, such as dysentery, which was the cause of his death.
His brother, John, Duke of Bedford was the perfect man to administer the dual throne, though as he was an able warrior and administrator but more than that, he was a francophile, and he did his best to not upset those French who were loyal to him, like the citizens of Paris. He implemented laws against any rogue English knights who were causing trouble, and he did his best to keep the law. That the throne eventually collapsed and Henry's territories eventually fell was not entirely his fault, but moreso because the French united more against the strung out English armies, and the fact that the Burgundians for a time reneged on their dal and made peace with armagnacs against the English, though were forced back into an alliance, they were never trustworthy allies. With Bedford's death, there was no longer anyone who could keep this throne together, and though John Talbot did an admirable job, the English were eventually swamped out by a united French force, and once the French Dauphin became sane, he proved to be a capable leader.
However a more sober assessment might look at which King introduced the most changes through Acts and culture and that would be more difficult to determine.
Tough, I would nominate Edward I.