In V.C. Letemendia's novel The Licence of War, which is set in the English civil war, and it is said that the protagonist's family was one of William the Bastard's Conqueror's Norman invaders, and were ennobled(is that the word?) by him following the conquest of England.
What I am wondering is though, if a 17th century English nobleman would be proud of his Norman, which, I would guess, would have been linked to the French, ancestry, seeing as the English had been in a rivalry with the French for centuries at that point. Would it be more prestigious for a noble to say that his family is descendent from a pre-Norman Anglo-Saxon noble family?
As ETFox alluded to in their answer, the situation's a little more complicated in terms of the 17th century view of the Norman past. While it's certainly true that noblemen were still invested in and proud of the depth of their heritage - and were still keen to emphasize their lineage - this was not because of the Norman ancestry so much as the legitimacy which antiquity offered to noblemen in a time where the creation of new offices of nobility (particularly the Baronet, through sales of which James doubled the number of lords) and the investment of titles in the King's favorites, most infamously the Duke of Buckingham, proved very controversial.
The Normans were not thought of as being the roots of the English civil past, however. As ETFox notes, the overriding instinct was the rediscovery of the "Ancient constitution" which had preceded the Norman kings, exemplified in documents such as the Magna Carta; this was the basis for works such as Smith's De Republica Anglorum, and the justification for the constitutional changes which followed the 'Glorious Revolution' of 1688.
However, the Norman kings were by no means reviled by noblemen. While the English Commonwealth did issue propaganda denouncing the "Norman yoke" (from which this idea originated), and claiming that with Charles' execution it had been lifted, this was founded on the idea that the English monarchy was a tyrannical imposition on the freedom of the English people (again an argument with European parallels in the Vindiciae Contra Tyrannos, Francogallia, the Dutch Act of Abjuration, and so on.
The wholesale destruction of the pre-Norman nobility by William meant that claiming ancestry pre-dating the Normans was practically impossible, and rarely done. Normans were not French, and indeed Normandy had returned to English hands sporadically up until the 16th century, and English claims had similarly not been renounced. So long as the premise that the monarchy was not tyrannical was maintained (and noblemen, whose authority was founded in the same system, had a vested interest in doing so), an English noblemen would not be ashamed of Norman ancestry; but his reason for demonstrating it would depend more on its extent than its provenance.
The rhetoric of the Norman conquest was certainly used for political purposes in the English Civil War. The Levellers in particular used the notion of returning to a pre-Conquest state of Saxon law in their material.