France and England, not France and Britain. From at least 1295 to the 1560's, Scotland was allied with France in a mutual protection pact in opposition to England, now known as the Auld Alliance.

French support for Scottish factions was also important in the 1715 and 1745 civil wars, although in this case Scotland was internally split between Hanoverian and Jacobite supporters.

It's hard to trace the origin but we can probably get close by looking at major events in the region:

Julius Caesar conquered Gaul and the following Roman legions moved on to Britannia. There would have been no conflict under Roman rule and, when the Romans left Britannia they still held Gaul for a long time and there is no record of undue conflict.

Charlemagne didn't turn his attention west at all so Britain was probably unaffected by his wars of conquest. While both France and Britain suffered raids from Vikings, Britain itself was largely dis-united until the time of Alfred the Great towards the end of the 10th Century.

So that brings us to William and his conquest of England famously in 1066 that led to decades of Norman French superiority over Anglo-Saxon natives and several wars thereafter. If I had to point to a single event, this was probably it.

EDIT: please look at sunday_silence's post

Exacerbating things were the English invasion and the disastrous (for the French) battle of Agincourt during the Hundred Years War and the French alliance with Scotland which was based in part on trying to dilute English influence over the region.

Hopefully others can expand in detail on the significant events especially the activities of Norman French lords during William's reign.

The battle of hastings in 1066 is a good place to start because a french speaking Duke, William the Conqueror from Normandy, from a section of what is now France, Normandy, came onto the English throne.

But even more interesting is what happened later. William's grandson Henry I had inherited the crown and died in 1135. His daughter Matilda claimed the throne but another guy Stephen of Blois also claimed it and there was a civil war that went on for about 11 years. Matilda had married a french guy Geoffrey Plantagenet from the Anjou province in France. He had been on good terms with Henry I, was knighted by him, married his daughter etc. He helped Matilda win the war and the parties agreed that Matilda/Geoffrey's son, Henry II would inherit.

So Henry II was successful both in England and also expanded his holdings in France so at one point they called his kingdom: THe Angevin Empire. at its height in 1172 it included most of the British isles and the western half of what is now France. French speaking rulers, we now refer to them as Plantagenets ruled England for over 300 years until the War of the Roses split them into rival families and Henry Tudor emerge as new King Henry VII in 1485.

So England had french speaking leaders for a long time with close connections to France. I dont think any of them spoke English well until probably the early 14th cent (but I could be wrong). Meanwhile, the Plantagenets lost most of their holdings in France pretty soon like the 13th cent.. But eventually there was a succession crises in France when the old king Chas. IV died without heirs in 1328. Ed III of England claimed the throne through his grandmother I think (after all the family was from France) and this set off the Hundred Years War. It wasnt like a modern day war where people fight every day; but really intermittent campaigns or raids, waged in France every few years. This went on with subsequent English and French kings till 1453 when the French finally succeeded.

This period saw armies go from feudal armies to more professional ones, and weapons like gunpowder had come about so that the middle class now had more of stake in war. Hence modern sense of nationalism was born. At the same time, through heroes like Joan of Arc, the French became a more centralized state and began to think of themselves as Frenchmen. Until then it was always one family or another constantly changing in power.

So you can see that these two regions had some connection through their Kings but then the inevitable succession crises led to fighting and rivalry. The 16th century saw the rise of Protestantism w/ England under Henry VIII (his father the first of the Tudor line in 1485) being a leading proponent and the French remained as Catholics were their polar opposite. By this time, the causes were set in motion that turned these kingdoms into what we now consider "nations" as well as rivals in the period of religious controversy that lasted through the 16/17th cent.

I guess by the 16th cent. or sooner, people thought of themselves as Englishmen instead of just someone who belonged to the Duke of Suffolk's manor who in turn who swore allegiance to someone who claimed England. In france, this probably happened a bit later, but by the time of Louis XIV (17th cen.) who expanded France's power and concentrated the monarchy the french thought themselves as frenchmen.

So the ground was laid for the next two hundred years (17th to early 19th cent.) as people now regarded themsleves as belonging to the English or French nation. So from Louis XIV to Napoleon England pretty much was Frances adversary on every occasion.