Roughly the same way it did to the OTL Angevin empire.
Flanders is not quite as threatening, speaking from the perspective of the so-called king of France (so-called given the weakness of royal authority), as Normandy and Anjou, but its not much better, either.
Not sure how an inheritance of all three would work - you'd need some lucky dynastic marriages of the sort the Habsburgs OTL exemplify.
Is there some reason for specifying Anglo-Saxon England? Not that I mind the idea, I'm just trying to think if there's a way that England would be different for purposes of the "empire".