Also remember the Normands spoke not only French but some kind of Norse. Still in Normandy there are Norse/Scandinavian names for places. Besides, Saxon and Norse languages must've been pretty mutually intelligible, even today German and Swedish is pretty similar even with a millennium or two apart.
There were a lot of cognate words and similar grammar, but genders and inflectional endings didn't match well at all. That drove the dramatic simplification of English grammar, for the most part. As for the Norman influence, it was mostly vocabulary... but changing the languages of documentation to Latin (mostly) and French (in law, for the most part) left English a lot of room to progress away from the Old English that was, by that time, already playing the same sort of role that Latin did in the Early Romance period - it no longer reflected the language that people lived in.
> There were a lot of cognate words and similar grammar, but genders and inflectional endings didn't match well at all. That drove the dramatic simplification of English grammar, for the most part.
It's why English nouns lost their masculine and feminine grammatical gender. The people who used both languages had more important things to worry about.
English doesn't quite meet the criteria of being a creole, though.
Superstratum/substratum theory applies here. English has an Ingvaeonic superstratum and multiple substrata, from Old Norse and Norman French at least, if not more.
