I don't think it's a coincidence per se, the languages diverged a long time ago and drifted away both in pronunciation and meaning.

My point is that false friends are blurring the border between the two languages in your brain, they are confusing because they make you think of something in the wrong language. A solution to reinforce the separation of languages in your brain is to only think about them in the context of their own language, as soon as possible.