Why exactly did France and England hate each other so much through the dark ages?

The short answer is "they didn't, because there was no 'England' or 'France' in any of the so-called 'Dark Ages'." The longer answer is a bit more interesting, though, so here we go.

Before 1066, there was no particular political enmity between France and England; simply put, England was (and long after remained) a relative backwater barely holding off Viking/Norse incursions, while the King of France was all but completely engrossed on the Continent. So, for the time that people typically call "the Dark Ages" (~500-1000), there was no particular hatred between the two kingdoms or its people.

After the conquest of England by William the Conqueror, Duke of Normandy (a region of Northern France), however, the King of England would control various parts of what would become France for many centuries. The conflict between the two kingdoms really took off towards the close of the Middle Ages with the death of King Charles IV of France in 1328, at which point King Edward III of England declared himself the rightful heir. The legal issue is somewhat complicated: there was no direct male descendant to succeed King Charles IV, and the nearest male descendant was Edward III through his mother; however, French succession law only allowed succession through the male line.

The conflict over the crown of France kicked off the Hundred (and Sixteen) Years' War in 1337, a war in which the English lost the vast majority of French territory to the French after nearly succeeding in taking the throne. The loss notwithstanding, English monarchs would continue to style themselves "King of England and France" until the 19th century.

All this aside, though, it's misleading to suggest that "France" and "England" hated each other in the sense we think of today: a hatred or distaste felt by the average citizen of both countries for the Old Enemy. In reality, the average person (of any class or gender) didn't consider themselves "English" or "French" in any case, and likely never traveled outside of a small radius around their place of birth. The monarchs and high nobles, for their part, were not at all concerned with national identity—they were closely related, of course, and indeed they had much more in common with each other than with their subjects. The wars were about power, succession, and dynasty, not national interest.

Actual enmity between England and France would not develop until the early modern period, as religious and linguistic identities became stronger and the two countries clashed over their growing empires.