Actually it's much more complicated than that. When William of Normandy invaded and took control of England, many things happened but there were two broad consequences of significance to English history:
1. The language of the English court changed from English to French, would stay French for the next 300 years give or take, and pushed English into the form used by Geoffrey Chaucer (Middle English), and
2. The English crown would have either land or claims to land on the east side of the channel, the subject of many wars, until the mid-15th century. These claims would not be ultimately resolved until after the Hundred Years' War, nearly four centuries after William's victory at Hastings.
The reason why the French and the English get along so poorly is because their histories are so thoroughly intertwined.
That makes sense.
It is a fascinating history; shortly before losing by a hari at Hastings (the Normans had almost given up), Harold had marched his army for days after defeating a Viking army at Stamford Bridge. The Vikings were a presence as well; Dublin was a Viking settlement. Their pure language is still spoken in the country with the oldest parliament, Iceland; I believe the “Althing” (spelling) is over 1000 years old.