I've been reading Sir Thomas Mallory's Le Morte d'Arthur and some peripheral stuff on literary history, and it seems to me that Arthurian legend was developed in large part by the French in the 12th and 13th centuries, an era of seemingly constant wars between the two countries. Furthermore, the French influence on Arthurian legend can be seen in English works during and soon after the Hundred Years War. Why did the French embrace a body of work extolling the virtues and prowess of a hero-king of an opposing nation, and why did the English adopt the French adaptations into their own literary tradition when there would seem to be so much animosity between them?
I hope someone answers this better for you soon, but thinking of England and France as two seperate nations in this time period, or even as nations at all, is problematic to answering the question.
You should remember that for much of the 12th and 13th centuries the wars were about one French dynasty who just happened to control England as a seperate monarchy due to inter-marriage and the Norman conquest fighting another French dynasty for the throne in Paris. Hence the kind of people on both sides of the channel interested in courtly love and adventure were French speaking nobles steeped in continental Latin history, who perhaps would have shared a similar exotic interest in a Celtic/Roman past on the pherifery of both kingdoms (much of the Arthurian legend being set around Cornwall, Wales, Ireland and Brittany after all).
Culturally the commoners and peasants of both kingdoms may have had differing oral traditions and myths and ideas about group identity, but this mattered far less for the nobility across Europe, and for those involved in the struggle for the French throne inpaticular, until we start to see national identity form after centuries of war closer to the 15th century that eventually bleed into the nobility identifying themselves with nationhood rather than a pan-european post-roman Latin culture