The Scandinavians also gave us our pronouns: they, them, their, she. Also a few common words: call, get, hit, husband, knife, law, leg, odd, same, skin, take, want, wrong.
English is classified as a Germanic language because of its grammatical structure. Its closest relative is Frisian, still spoken in the eastern part of the Netherlands. French had a great influence on English, but mostly in contributing a lot of words to English. However, French did not for the most part alter the grammar of English.
For example, like all Germanic languages English has modal verbs: will, would, shall, should, may, might, can, could, ought. French doesn't have these modal verbs, though it expresses the same ideas with its verb system derived from Latin. Also English has a progressive tense: I am going, I was going. French doesn't have a progressive tense. Also, English usually places the adjective before the noun. Except for a few common adjectives, French usually places the adjective after the noun. And look what I just did with the adverb "usually". I put it before the verb. French wouldn't do that. And there are a lot of other reasons for classifying English as a Germanic language and not a Romance language like French.
Yes, English borrowed thousands of words from French during the Norman occupation of England. But now the current is flowing in the other direction. This is why you find the words "le parking" and "le jogging" and "le big" and many others from English in French today.
I was taught in the English elementary school system all too many years ago. The English school marm made history absolutely a class to be enjoyed. The kids would declare their favourites. Yes, Harold,last of the Saxons Kings, was the hero. How we wished the result of the battle (Hastings 1066)could be changed. Curiously enough the kids all sided with Joan of Arc, the immortal French woman. I cannot remember how the teacher explained that one. (laughs)
One could introduce the Welsh factor at one's peril. I have a birth certificate for someone born in Wales 1875. The modern copy has it in both English and Welsh. Never a more striking difference is in the two languages. One could throw into the mix, that the Welsh could claim to be an indigenous people. Hard to classify these persons with the rest of the British Isles.
Yes, the French authorities getting testy over the "rude" and direct anglo names. Touchy lot, well to me anyway. English snobbery delighted in using French expressions for many years. Beau Brummel comes to mind- a raconteur with his Bon Mots, I believe.