There are currently no FF3 mods for any 3D version of the game. Platform-specifically, the PSP version of FF3 uses the same model textures as the PC version, though the HUD/Menu images and pre-rendered videos are quite a bit lower res, and I suspect the frame rate is lower. But as far as I can tell, in all versions of the game, the textures are rendered with nearest filtering which looks pixelated and retro. For such LQ textures, PPSSPP has this amazing form of texture filtering called xBRZ Hybrid Bicubic that makes all images and textures in the game look smooth and sharpened, in a way that currently no other version of the game can. For the most renderer-specific graphical-enhancing mods, I suggest buying the PSP version, applying any necessary language patches available if it's a foreign copy, dumping the ISO to your hard drive, installing the latest build of PPSSPP, and then depending on your computer or tablet's graphics capabilities, running the ISO on PPSSPP with various graphics enhancement settings. Personally, when I'm focusing on quality rather than maximum performance, I use 4x resolution, 16x AF, 5x Hybrid Bicubic Upscaling, and Natural/FXAA post-processing shaders.
3D remakes of both Final Fantasy III and IV have been released for DS, PC, iOS, and Android devices.