A few days ago, a friend of mine (herself ABD in English literature) was told that it’s only natural that she writes English like a native, since her mother tongue is Spanish “and English is a Romance language after all”.
OK, jokes aside: it is undeniably true that if you go by vocabulary origins, the vocabulary of an educated native speaker, or the 80,000-odd entries in the Shorter Oxford Dictionary will have a plurality or even a majority of words of Romance origin.
But remember: many Latin- (and Greek-)derived words are actually part of the educated speaker vocabulary in most Indo-European languages—particularly scientific, medical, and legal terms. This is not unique to English.
The “operational definition” of a Romance language, according to most mainstream linguists, is a direct descendant of Vulgar Latin — the colloquial counterpart to the classical written language. After the [West-]Roman Empire fell apart, the various dialects spoken in Italia, Gallia, Hispania, Lusitania, Dacia evolved into separate languages that we now call Italian, French, Spanish/Castilian, Portuguese, and Romanian, respectively.
In contrast, Old English developed mostly from Germanic sources — the speech of the Angles, Saxons, and Jutes, with later the addition of Old Norse from the invading Vikings. If you read Beowulf in the original, you (a) will need a dictionary or a parallel translation; (b) if you’d mistake it for any language other than English, it’d likely be something Scandinavian.
Hence, the oldest and most commonly used words — what in Hebrew we call the Elef Milim [“One Thousand Words” language primer] vocabulary — are about 83% Germanic in origin.
What about the Celtic language spoken by the ancient Britains? It used to be received wisdom that the Britons were wiped out by the invaders, but recent genetic studies have shown a surprisingly small percentage of Anglo/Saxon/Jute genetic material. John McWhorter, in his book Our Magnificent Bastard Language, explains that in all probability, the invaders were (nearly) all male, took wives from the Britons, lorded it over them — and the Britons assimilated into the new society. Now as he explains: usually when you learn a new language as an adult (through immersion rather than formal schooling, at that), even if you learn the vocabulary fairly quickly, the grammar and syntax of your native tongue tend to stubbornly persist. As a result, English to this day has some grammatical peculiarities that are unique among the Germanic languages but can be found among the Celtic ones: for example, the interrogative, emphatic, and negational uses of “do” (“Do you like chocolate?”, “I did do my homework”, “I don’t like mondays”.)
The transition from Old English to Middle English — from the English of Beowulf to that of Chaucer’s Canterbury Tales, if you like — is conventionally marked at 1066, the Norman Invasion. And yes, as you can see from the pie chart above, William the Conqueror/Guillaume le Conquérant and his nobles did leave their linguistic imprint on English with a vengeance. It took until Henry V for England to have a monarch who was more comfortable speaking and writing (Middle) English than French!
But, crucially, the core of English remained—both in vocabulary and in grammar. For instance, English proudly sports three grammatical genders — male, female, and neuter — unlike all Romance languages (except Romanian, sort-of) who appear to have inherited their dual gender from Vulgar Latin. (Classical Latin of course did have a neuter gender.) And what typically happened when the Old English word met its Norman French counterparts, is that the language has preserved both — sometimes as synonyms, sometimes as different nuances or usages (e.g., sheep/cow/pig for the animal, mutton/beef/pork for the meat).
Early Modern English — the idiom Shakespeare wrote in — was ushered in by two phenomena.
First there was the introduction of the printing press to the British Isles by William Caxton: after the Reformation, this enabled the first widely spread printed books, namely the Book of Common Prayer and later the King James Bible. This greatly accelerated the process of standardizing the written language, like it did in other European countries (cf. Statenbijbel for Dutch, Lutherbibel in the Protestant parts of Germany,…).
Second, during the English Renaissance, authors seeking to show off how well-read they were imported Latin and Greek words by the galleon load. (This happened to other languages as well, but perhaps less egregiously so.) Oftentimes, the “learned” synonyms coexist to this day with plainer English words—in some cases making the latter ones “quaint” and “archaic”.
Of course, words were absorbed later from English colonies (veranda, pajama,…) and from foreign professionals (e.g., many nautical terms in English are Dutch imports, like schooner, lee, starboard, keel,…) But in the larger scheme of things, these have affected only English vocabulary, and only at the sub-percent level each.
Structurally and in core vocabulary, English is and remains a Germanic language that just happens to merrily assimilate extended vocabulary from any and all sources — the two main ones undeniably Romance. I really like McWhorter’s term “Magnificent Bastard Tongue”.
Finally, there are researchers who have sought to quantify the degree of kinship between languages — see, e.g., this non-paywall overview paper by Maurizio Serva. The metric used is typically the Levenshtein Distance between lists of the most frequently and universally used words — these 100-word or so “I have a little list”s are still an order of magnitude smaller than the 1,000-word corpus mentioned above. A “family tree” of Indo-European languages constructed in this matter firmly places English in the Germanic group—nearest to the Scandinavian languages, in fact. This is Fig. 1 from Serva’s paper: