Did the line of William the Conqueror ever intermarry with the families of the old Anglo-Saxon kings?

Answer 1

William's wife, Matilda, was a descendent of King Alfred the Great, an Anglo-Saxon king of the late 800s.

Answer 2

Would this site help you answer your question? http://www.electricscotland.com/history/dumfries/history2.htm

This is one of the paragraphs which mentions the families of the Anglo-Saxons....
"Some of the Norman chiefs followed them, as we shall see, at a later period; and the races who were at fierce antagonism in England, manifested no such feeling towards each other when they met further north. Many families who subsequently played a distinguished part in Scottish public life, were founded by these Saxon or Norman settlers, and some by a union of both. Especially was this the case in that portion of the kingdom to which this history relates."