I find a good way to show how thoroughly Germanic English is, is to split up how you look at it. There are several ways you can stack up English against Proto-Germanic, French, and so on. The big three ways, I'd say, are syntax (how you string words together); morphology (how words get their endings, like 'way' > 'ways', 'go' > 'going'); and vocabulary (words).

Syntax is hard to stack up, but the others are easy.

The morphology of English is roughly 100% Germanic, not Romance, Latin, or Anglo-French. English does have a handful of un-Germanic endings, like 'radius' > 'radii', but they're few and far between. And you meet them less and less often these days: I think you'll hear people saying 'radiuses', as much as 'radii'.

Vocabulary is also a biggie. If you look at a catalogue of words, you'll find that over 50% of the headwords come from Romance or Latin. And that seems like a lot. But that's just a catalogue. If you look at a string of words, an ongoing chunk of something someone has said or written, you'll almost always find that over 80% of the words are Germanic.

This is partly because nearlly all 'function words' in English are Germanic, including all pronouns (I, you, they, we, us, it); articles and demonstratives (a, an, the, some, this, those); nearly all prepositions (up, over, beyond, through, of, by). And it's partly because Germanic words account for a huge proportion of the most common other kinds of words.

Let's take an example: your own question. Here's a marked up version of what you wrote, with Germanic words and endings highlighted in orange, Romance/Anglo-French in blue, and Greek in green. You'll see that most of your question is orange -- Germanic.

If we count only words that you yourself wrote, and not the subreddit name and so on, and we exclude all proper names, there are 97 words in your question. Of those 97, a full 86% of your diction is Germanic. Only 12% is Romance (I'm counting 'because' as half Germanic, half Romance), 1% is Greek (the word 'dialect'), and one word is of unknown origin ('bar'). And 100% of your word endings are Germanic (-ly, -ed, -s).

Another way of illustrating just how Germanic or how Romance English is, is to see if you can put together whole sentences using only Germanic vocabulary, or only Romance vocabulary. As a sample, go back and re-read the first four paragraphs of my answer: they're virtually all non-Romance words. The only Romance word I used was the word 'vocabulary', and the example of 'radius'. (There are a few Greek words, too, which may seem like cheating ... but you didn't mention Greek in your question.) I defy anyone to do the same using only Romance vocabulary!

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Edit, a day later: I now realise a Romance word slipped past me -- 'people', in my 3rd paragraph. Dammit!

First off, even though you can only pick out a few words doesn't mean there aren't a lot more words that survive in modern English, it's just that their pronunciation has shifted around a lot. For example "genog" is the same word as "enough" with some twists of pronunciation even though you can't pick it out.

For example look at this line of the Lord's Prayer: "Fæder ure þu þe eart on heofonum; Si þin nama gehalgod." Looks like gibberish at first glance but if you break it down word by word (note "þ" has a "th" sound as in "Thor"):

Fæder = father

ure = our

þu = thou

þe = that

eart = art

on = in

heofonum; = heaven

Si = be

þin = thy

nama = name

gehalgod = hallowed

A lot of these words look very strange but they're the direct ancestors of English words we use today (or at least used LONG after the Norman Conquest), they've just changed a bit. Also a big part of the reason why, say, Beowulf looks so alien is that after it was composed English was influenced a great deal by Old Norse, which is another Germanic language. This is a big part of why older Old English (i.e. stuff from right before the Norman Conquest) is a lot easier to puzzle out than Beowulf.

Of course that doesn't mean that there wasn't a massive change in the English language with the Normal Conquest. We can roughly break down this change into three categories:

1. Changes in spelling and pronunciation. Often Normans and Anglo-Saxons spelled the same sounds differently so a lot of the changes look bigger on the page than they were in actual speech. Of course some Old English sounds (some of the guttural back of the throat sounds that are preserved in silent "gh" spellings in modern English) that didn't exist in French were dropped as well.
2. Changes in grammar. Mostly English became less inflected. For example "run" can change to: run, runs, ran, and running but the Old English equivalent could be changed in more ways, the same goes with other parts of speech. However this didn't make English into a Romance language as there is plenty of inflection in French and other Romance languages.
3. Introduction of lots of Normal French vocabulary. However the bulk of the most commonly used words remained those with Old English ancestors.

Of those three, the third one is the only one that really made English much more of a Romance language and, according to the way that linguists categorize things, the introduction of a whole bunch of new words alone isn't enough to make a language jump language families. However some people do categorize Middle English as a Old English/Norman French creole but that's not the consensus view.