Though even without the norman influence, Modern English would be no different than its current form:
That's untrue-- there are aspects of English in all domains from phonetics through semantics that are due to Norman and other influence. We didn't just borrow words from other languages, although that's the most obvious area: less than 40% of words are "original English". (But all of the words are certainly now English!)
ie. would no-longer resemble Old English
Icelandic, the most isolated of the Germanic languages, is remarkably similar to Old Icelandic (basically Old Norse).
There's no question that it would look a lot more like Old English without Norman influence. But certainly there would be changes as there are in all languages.
One major question to ask is whether some of the radical simplification of morphological paradigms is partially caused by language contact. McWhorter's (2007)
Language Interrupted certainly claims so. He argues that modern English looks as it does specifically because of the effect of adult L2 learners simplifying it.
While that may be controversial, it is not possible to simply dismiss foreign influence as only some kind of dilution of the vocabulary. There's a lot more going on. In fact, one might even go as far as to call modern English a creole (mixed language), though that's an extreme claim. But however we phrase it, Modern English is what it is because of contact, at least to a substantial degree.
I believe that there are three major differences that cause Old English to be unintelligible for speakers of Modern English:
1. Lexical changes.
Unquestionably caused by contact.2. Simplification of morphological paradigms (such as subject-verb agreement being all but lost and the loss of nominal case except minimally for pronouns). (This also then lead to more rigid word orders, which is another fairly major change, although it doesn't make OE all that hard to interpret if you read it slowly and know everything else.)
Possibly caused by contact (cf. McWhorter).3. The Great Vowel Shift: this is the main reason why our words sound different from Old English words (but not the only reason). This started less than 300 years after original contact with French and during continued contact.
It probably wasn't directly caused by contact, but it is certainly the result of restructuring after that contact based on the state of the lexicon at that time.(The orthography is also somewhat different, but that's not a factor for spoken language and it's not especially hard to read Old English if you know the rest. I don't consider that a major change, and even so it is partially caused by contact with French [and other languages] and mixing of several spelling systems.)
So in summary, most of what makes Modern English "modern" is actually contact with other languages. While ME wouldn't look just like OE regardless, it would probably look different in other ways and overall quite a bit less different-- it would probably be something like Old High German and Modern High German. English would, in short, look something like Dutch. Contact with Celtic, Scandinavian, Latin and French is specifically why English is not very much like Dutch today. (Actually, it would probably look a little more like Frisian than Dutch, but close enough-- it wouldn't be very different from either.) Within Germanic, English is very weird because of this. In many ways it just doesn't feel Germanic (though it does sound mostly Germanic overall).
Further, Germanic itself is probably how it is due to contact (with probably Finnic, Celtic and Slavic languages, among others). Consider Grimm's law (Spanish
pes and English
fish where p>f, and many other similar consonant shifts)-- to truly eliminate all traces of contact we should go back to Proto Indo-European. But of course that must have been in contact with other languages too!
So again this is an interesting thought experiment but completely artificial. In fact, it would be simpler to eliminate all Germanic words from English, although that would be a problem for some of the most basic words like "to be" with no obvious substitute. We can almost do that intelligibly right now though with "fancier" borrowed words used in place of common Germanic roots-- consider "nasal cavity" or "nasal appendage" for "nose", which is a little unusual but completely intelligible. (And we'd have to decide what to do with the core function words that are entirely Germanic.) Doing the reverse is near impossible without substantially supplementing the ME vocabulary with resurrected archaic words from OE and coining new words from Germanic roots.
I tried to check out the video but Youtube says it isn't available (as if it was removed by the author or for copyright reasons or something like that).