What does authentic mean in this case?
For basic translation there is usually a distinction between literal, liberal and pizza cats (named for the cartoon that took the animation and made up its own stories to go with it, not so commonly seen in games unless we are counting spoof stuff as a means of translation, though that would be amusing to see).
Pure literal can be a bit clunky to read if not done exceptionally well (as in any poems translated have the same rhyming scheme) so people usually accept a bit of a clear up there for legibility in games (it is not like this is patents, legal transcripts or healthcare records) even if going more for literal.
Liberal translations tend to remove say elements of Japanese culture/pop culture that game devs might include, or tone it down if the original is just supposed to be in a city and not have an air of the exotic about them (while today sushi, ramen and the like are popular, maybe even staples of diets, outside Japan there is still an air of the exotic), some may go further still and inject their own pop culture references, jokes and the like (Japanese wordplay is hard to translate, though if it is in service of telling a joke in the game itself then you can often do that instead).
In the case of Final Fantasy you also have the decision of what terms to use -- many things are common to games in the series but only got established later.
Do you have a preference for platform here? The NES version has never seen an official translation and I have not read a comparison between that and the DS version for the main story parts, the DS version however getting a load more fluff, sidequests and other flavour text. The DS version is the basis for everything that is not an emulated NES version, which is to say IOS, android, psp, PC, windows phone and ouya. I also don't know if anything got tweaked for those further releases in terms of meaningful text -- some of the online functionality of the DS version was dropped in favour of a sidequest). The DS version does however change up a fair few gameplay elements compared to the NES version.https://finalfantasy.fandom.com/wiki/Final_Fantasy_III_version_differences
) is anything to go by there might be some scope for a restoration effort for the DS version somewhere down the line.http://www.romhacking.net/?page=translations&genre=&platform=1&status=&languageid=12&perpage=30&order=&dir=&title=final+fantasy+3&author=&transsearch=Go
should yield all the versions available (I don't think the DS version, or anything spun off from it, has ever seen any retranslation efforts, mostly just save editors).
There are three main choices then for the NEShttp://www.romhacking.net/translations/141/
The main one people look to. Some parts condensed a bit to fit in the game.http://www.romhacking.net/translations/1590/
Might not work on all emulators and flash carts but has some extras and should not otherwise full.http://www.romhacking.net/translations/4760/
Might be the best of both worlds as far as working on various emulators and flash carts, though some aspects for naming might bother depending upon what you are looking for.