To be honest - if I'd been translating the game, and the developers had come back to me and said "No, it should be
Aerith, not Aeris. Because it's based on 'Earth', right?", then my response would have been "Well, you're the boss. But ... you crazy, man. Maybe that works super well in Japanese, but if you're wanting to imply this name is something to do with earth, then
both of those options are rubbish - because they begin with 'Aer', which is basically the root of probably
hundreds of words in European languages that are all to do with
air. But, you know, if you're stuck on this 'Aerith' thing because that's what you've already decided on, then fine..."
Evidently 'Aerith' is what the writers intended. Of course, there's sometimes a difference between what the Japanese authors decided on, and
the impression it makes in English...