But actually I've made the mistake because in Russian the transliterated version of the would start with the same letter as the one of zooOnly if you want to sound like you're putting on a (bad) French accent. No native English speaker would naturally pronounce 'the' with a z.
Yes, this happens. The point is that no two languages in the world have exactly the same phonetic systems, and the English and Russian alphabets have very many points of difference. Russian has single letters that in English need two or even four letters to express them (like ts, ya or shch). Standard transliteration systems can only go so far.... in Russian the transliterated version of the would start with the same letter as the one of zoo