If following strict French pronunciation rules, it should be pronounced [ʒina], and some native speakers (in my experience mostly older, monolingual folks) would indeed pronounce it this way.

That said, most native speakers at least try to mimic the original pronunciation of proper nouns

Souvent les noms étrangers sont connus d’abord par écrit, et les français reconstruisent une prononciation vaguement étrangère en se basant sur les langues qu’ils connaissent et en essayant d’éviter les lettres muettes. (Gilles, 2011)

So, in that case, I and (I suspect) a vast majority of native speakers would render something close to [d͡ʒina].