William the Concurrer just got to initial stuff.
I don’t think the Bastard was closely related to the Saxon kings. The Normans at that time were only a few generations removed from their founders, the Norwegians, and weren’t mixing with the Germans. They mixed later, after the Norman Conquest of England-and-a-bunch-of-other-places.
Edward and Alfred's mother was Emma of Normandy who was the sister of Richard (II) the Good of Normandy, Richard was also the father of Robert the Magnificent who was the father of William.
So they were second cousins. Or first cousins once removed. I can never keep those straight.