You're rewriting history here. "The normans" were completely integrated in the French aristocracy, and that's why the kings of England took part in the successoral struggle. The 100 year war was started by the grandson of Philippe IV, of the french Capet dynasty, fighting against a nephew of Philippe IV for legitimate motives. Other cousins fighting it out included the dukes of burgundy, the house of Anjou-Sicily, etc.
If anything, a few normans lords marrying into the Capet family was just a little gene refill to stave off inbreeding.