Personally I am not particularly fond of remakes in general - I feel like they are often made just to cash in on the original title, rather than actually making necessary improvements.
One game that I would love to see remade is Silver Surfer for the NES - that game seems to have potential as a good space shooter, it just has a handful of annoying problems that kind of ruin the game, like for example the huge Silver Surfer sprite, the limited movement on overhead stages, the lack of an autofire button and the ambiguous foregrounds and backgrounds.
If those relatively simple things were fixed, then it would suddenly be a fairly good shooter.
The overwhelming number of enemies and the one-hit-deaths shouldn't be huge issues by the way, because most space shooters are like that.
Anyway, if they are gonna remake FF3 then they really should give it the same high-class makeover as FF1 and FF2 on Final Fantasy Origins, with roughly the same graphical style - in fact, I think that a remake like that should be part of the Origins collection.
A collection of the "classic" FF games that only includes FF1 and FF2 and completely ignores FF3 really feels kind of incomplete, and I always found that mildly irritating.