Yes, but as head of a multinational hereditary empire, might he not be expected to spend most of his time where the trouble is, or at least subjugating the smaller neighbors whilst the big, hulking rival (i.e. France) is not focused on knocking you off?
One might argue that the marriage of Ed II and the Princesse de France was the sort of dynastic alliance you'd expect to see if Ed was going to move against his other neighbors. It doesn't make him "English"--he most likely spoke very little, if any for one thing, and the language of the court, when not French, was latin--it makes him a good dynast and ruler looking to expand where opposition is weakest.
Merely because he held the title King of England doesn't make him English any more than the Norman kings of Sicily are Italian or Guy de Lusignan (I think I have the name right) was Armenian. He was a French peer who had powerful holdings outside France.
Furthermore, an incident is recounted wherein a chronicler with the young Ed. I on crusade in the holy land heard him mutter a couple of words of English, which was considered rather unusual. His Official biographer noted of him, "he can scarcely be looked on as an englishman."
Upon the death of his father, Ed. I went first to Paris to swear homage to France, then to Gascony to spend many months putting down the rebellion of Gaston de Bearn. Only then did he bother heading up for an English coronation.
England was a crucial piece in the Plantagenet Empire, but arguably Normandy was more important, as it was the nexus of communication lines between London and Bordeaux.
To view the Plantagenet realm as England plus a few French counties is to follow the nationalistic and narrowminded Whig interpretation of History. It simply isn't true. Going back a little furtehr but still in the CK Timeframe, Henri II spent 14 Weeks in England vs. 38 in France in 1170, the year of Beckett's murder. That year, he covered over 2000 miles travelling around his realm. In fact, that year he arrived in England on 3 March. This "English" King hadn't set foot in England in 4 years!
If it looks like a duck and sounds like a duck and acts like a duck, it's a duck. If it looks French and it sounds French and acts French, it's French.
