. . . . Last night:
Before and during and after William the Conqueror's time, the Norman duchy wasn’t very peaceable – those Norse, and those Norse kiddos! – as various sons, legitimate and bastards, and other rebellious factions fought over possession.
During the Conqueror's own rule there was dispute between two of his three sons as to who would have Normandy and / or England.
William Rufus, i.e. William II and Robert Curthose II both demanded possession of duchy and the kingdom of England. Their conflict was only repressed by the Conqueror himself.
Further, the French king, Henry I schemed, promised and intrigued with the Conqueror's sons to turn them against this powerful, vital, energetic ruler who had conquered England -- whether with or without the Capetian monarchy's approval (it was a regency at the time, under the control of the child king Philip I's mother) and encouragement (the deceased Henry's brother Odo and his army enthusiastically participated in William's invasion). The pope seems to have given his blessing to the enterprise only after the fact.
. . . .This is the delightful part, which provoked minutes of laughing: after the death of the Conqueror's death, his oldest son, Robert Curthose II, PAWNED the duchy of Normandy for 10,00 marks (which, somehow he never repaid – did he pawn Normandy to Jewish merchants?), the duchy which had been ceded to William Rufus! -- to finance Robert's participation in the first Crusade. Imagine!-- pawning a duchy, like your dad's old gold watch! I just couldn't get over that.
Before Robert returned from Crusade, William Rufus had gained possession of Normandy with the help his father. When both father and Robert died, he got England too, but England did not like William Rufus. Additionally, William II seems to have been a lazy and inattentive English ruler, and ultimately the younger brother, Henry, got the crown of England on his own head, partly via intrigue, diplomacy and purchase, becoming England's first Henry.
We see every variety of the English - French inter and intra bloody quarrels for the coming centuries already in place at this point, if not before.