Would English have ridden itself of ‘-est’ and ‘-eth’ whether or not the Normans invaded?

What the title says. Est and eth were fayed to doing-words to make their singular second and third person present conjugations. Old English had them, and so did Middle English, and even until not long before now, Modern English had them. Did Anglo-Norman or French in any way stir it to fall? Also, it has been hard to find samewords for a good deal of grammatical jargon. Any tips?