No, Old English is pre-Norman invasion. I think you have (understandably) misunderstood what a "negative concord" means--it's when a double negative is still a negative, ie multiple negative elements agree with each other rather than cancel out. Like "I didn't hear no bell". A lot of languages are like this (eg Spanish).
In the OP article the sentence has both this "ne" and also a "never"
From what I’ve heard on “the history of English podcast”, after the Norman and invasion written English disappears completely for about a century. This is because the clergy and lawyers were the only literate people at the time, and they were all French. When it re-emerges, it doesn’t have much French in it yet, because only the common folk spoke English, and the norman upper class spoke French, and they didn’t interact that much. It actually took another 100 years or so for French words to percolate into the language.
What I learned from the podcast was that what really changed old English into Middle English was the viking invasion around 800. Danes and anglosaxons had different grammar and as a compromise a lot of the germanic cases on nouns, which allowed for arbitrary word ordering in a sentence, got discarded, and English developed the current emphasis on strict word ordering that we have today.
