English lost it’s gender and most of it’s verb declensions as a result of the Norse occupation. The Norse occupied around half of Britain for several hundreds of years. Both Norse and English had these linguistic forms, but the specifics did not match and were confusing to the adult Norse trying to learn English. They adopted a simplified version and that spread among the population.

The grammatical effect was stronger than the Norman influence because the Norse lived among the English unlike the Normans who were a ruling class.

The Norman influence was more in the vocabulary and spelling. Normans were the scribes, lawyers, etc. They introduced large numbers of Norman French words that trickled out into English. Their scribes used French spelling even when writing English words. That is part of why English spelling is so complex now.