English does not descend form Old Norse (a North Germanic language). It was merely influenced by it due to Viking invasions of the British isles. English is a West Germanic language more closely related to Frisian.
Old English is definitely West Germanic. It's much less clear whether Middle and current English can be considered more West Germanic or more North Germanic; there's still a debate raging on.
There’s not really a debate among linguists. No amount of Old Norse loan words can justify reclassifying English as North Germanic.
As far as grammar and syntax are concerned, Old Norse had some interesting effects such as influencing leveling of noun declensions but generally these are just simplifications of native English grammar and not imports from Norse (which had a full on conjugation system). The borrowing of certain Norse pronouns into English is probably one of the most extraordinary changes.
Another angle is to look at sound changes. English has shared sound changes with other West Germanic languages, while there are sound changes in North Germanic that English lacks. Compare the initial consonant cluster in West Germanic words for shield:
There are some people who argue Middle English is a creole [1] due to the massive influences from Norman and Old Norse but to say it’s North Germanic (or even Romance?) is pretty incredible. The implication would be that the British Isles spoke a form of Old Norse which absorbed almost all the features of Old English, which is not what our written records show. My understanding is that even the creole theory is not widely accepted among linguists due to some features of creoles that are missing in English (e.g. standardization of irregular verbs, irregular plural nouns, …).
It is still a contested topic among linguists, I keep seeing newly published articles about it. The debate's mainly around whether the standard used for Middle English writing is Anglicised Norse versus Norsified Old English. I've seen strong arguments for both views. If you know English history or know English dialects then viewing some types of English as Anglicised Norse would not be surprising.
