So for me, as I stumble and bumble my way through learning French (mostly through DuoLingo, hey), I'm often thinking about this issue.
Now-- on the surface of things, Modern English is almost exclusively comprised of German & French, and almost every word in these sentences are specific examples of such in terms of direct etymology. Which is a big part of why I've typically regarded French & German as my sibling languages. It's a nice, bright thought, anyway!
Let's take the modern English word "fight"-- WP claims:
From Middle English fighten, from Old English feohtan (“to fight, combat, strive”), from Proto-West Germanic *fehtan, from Proto-Germanic *fehtaną (“to comb, tease, shear, struggle with”), from Proto-Indo-European *peḱ- (“to comb, shear”).
My point is that there's so many ways to run with that over time... in any language whatsoever! Indeed, IIRC there was a "fisten" variation which meant an entirely different thing in earlier German.
But, "shear?" Yes, yes back in my schoolyard days, I wanted to shear my opponent like a little lost lamb, but... I don't think that's right.
So here's my point, assuming you've lasted this far. Modern German in fact split from modern English maybe around ~~800AD? And Modern French, around... perhaps slightly earlier than the Norman Conquest (1066), meaning that even though Modern English is absolutely PACKED full of French & German pronyms, we can't just assume they mean the same thing, anymore, as with the examples above.
It sort of breaks my heart, but it's just reality, non?
Semantic drift always makes such a mess of cognates. One of my best examples of that is an etymological triplet in Portuguese:
All three were originally the same word with the same meaning. Borrowing here, borrowing there, and now they're three different words with completely different meaning.
A good reference date would be 450 or so, when the Jutes, Angles and Saxons invaded Britannia. It's what created the geographical barrier between Germanic speakers, that allowed English to diverge considerably more from continental varieties (Frisian, Dutch, German "dialects" [actually local languages]) than it could otherwise.
For the French borrowings it's complicated because they didn't enter the language only once as a "nice set", but across centuries. And they weren't from a single Gallo-Romance variety but two (Norman and French).
And often the very fact that they've been borrowed changes the meaning. A good example of that is French ⟨porc⟩ pig, pork; it can be used for both the animal and the meat, but once English borrowed it as ⟨pork⟩ it was mostly used for the meat only, with then the old word ⟨pig⟩ being specialised to the animal.
Sorry for the late reply, but I love it!