It began in 1066 when William the Bastard, Duke of Normandy, won the battle of Hastings and had himself crowned King of England. He retained the title of Duke of Normandy, however. This put him and his heirs in the odd position of being kings in their own right, and also owing fealty to the King of France for lands they held in his kingdom.
Later this got more complicated. Henry II married Eleanor of Aquitaine and thus inherited Aquitaine - and by the late twelfth century English Kings controlled more land in France than French Kings did. This made the French very unhappy, and resulted in a string of wars.
The two houses also intermarried regularly; and around 1340 Edward III of England decided that he was also the rightful King of France. Cue the Hundred Years War.
By this time, of course, England and France could never get on. English kings and queens claimed the throne of france right up to the sixteenth century, and the last English possession in France (Calais) didn't fall to the French until 1550-odd.
By the eighteenth century, the decline of Spain left England and France the two superpowers in Europe; and since no-one had invented the Cold War by then, they fought a series of hot ones.
This only really came to an end when they found it to be much more fun (and expedient) to join together to fight Russia (Crimea etc) or Germany.
Then came the EEC. It is said that war is the continuence of politics by other means. The EEC reversed this. England and France no longer shoot at each other, but we're still firm enemies. The battlefield is now in Brussels (quite near to Waterloo, ironically).