You are correct in observing that German is probably the only language to *still* capitalise common nouns. (Note the emphasis)

First of all, this is because capitalisation can only happen in scripts such as Cyrillic, Greek or Latin which distinguish between capital and lower-case letters. Why they do that can probably be traced back to Charlemagne who let lowercase letters be invented — but that's a story on its own (and for a different Stack Exchange). Point being that the vast majority of languages out there use an entirely different script and thus cannot capitalise anything.

Sometime during the Middle Ages to Renaissance, capitalisation of some nouns, later more, became popular across many European languages. At some point in time, most of them would capitalise at least some common nouns.

In the following centuries, it became fashionable to drop capitalisation again. I think Danish was the final language to drop common noun capitalisation in 1948.

But of course, the discussion of English capitalisation rules (*English, Queen Elizabeth, Wednesday*, cf French *anglais, la reine Elizabeth, mercredi* and German *englisch, Königin Elisabeth, Mittwoch*) also warrants discussion.