Proto-Indo-European *yeuH "blend, mix food" in the suffixed zero-grade form *yuH-s- became Latin iūs "juice, broth", and French jus. This came to be spelled juice in English; ce replaced s in many words by analogy with French, even in words that were not spelled that way in French.
The form *yuH-s-mā- became Greek ζύμη "leaven". This was combined with ἐν "in" and was borrowed as enzyme, which first meant "The leavened bread with which the Eucharist is administered in the Greek Church".
The biochemical term enzyme was apparently borrowed from modern Greek ἔνζυμος "leavened".