I apologize in advance that this is somewhat brief and surface level, as I'm on mobile, but I'll focus on the Norman impact per the conquest of England. The Normans you describe were from the French region of Normandy but actually descended from vikings that Charles the simple of France had allowed (arguably under some duress) to settle there just over a hundred years prior.

Skipping ahead to 1066, William the Conqueror, then Duke William of Normandy, laid claim to the English throne via his mother's bloodline and relation to the recently deceased Edward the Confessor of Anglo-saxon England. William also claimed that the king Harold (appointed by the anglo-saxon lords and theoretically Edward as his successor) had relinquished all claims to the throne years prior while in William's captivity. The validity of the claims is somewhat shaky, as the primary sources we have are clearly biased (see the Bayeux Tapestry, commissioned by William's half brother the Bishop Odo, or the Anglo-Saxon Chronicle to capture each viewpoint).

Regardless, William prepared an army to invade England and though Harold was initially preparing for that attack from the south, William had to hold off due to inclement weather. In that timeframe, Harold Harefoot of Denmark invaded from the North, bringing our English Harold's armies up to meet them. William then made an easy landing and was able to push inland without too much difficulty until Harold was able to return south and face him at Hastings. Ultimately Harold died (per the bayeux tapestry by an arrow) at Hastings, and William won the day. Though he faced numerous revolts in the next few decades from the anglo saxon lords, he and his sons were eventually able to subdue England and Wales and bring the french language and norman culture to most of the nobility. This is largely responsible for the heavy overlap in vocabulary between english and french. If is worth noting that it did not affect the larger populace to quite the same extent, and wasn't quite genetic displacement as so much as just replacing the anglo-saxon noble classes with Norman lords. [EDIT to add that this meant many Norman nobles and the king of England had land both in France and England, which in a few centuries would contribute to the causes of the hundred year's war]

The Domesday book (a survey of landholders commissioned by William) is an interesting resource to see both some changes in ownership and also William's attempt to show continuity with Edward's reign. The many references to "TRE" are tempore regis edward, indicating the state of ownership now versus in the time of king edward. I did a fair bit of research on the history of the british identity as an undergraduate, though it's been a little while, so feel free to message me if I can help provide more detail. I'd strongly recommend looking into translations of the anglo-saxon chronicle and work by orderic vitalis as well as the domesday book and bayeux tapestry as primary sources, though be aware of their inherent biases