In order to sim the FF world, you have to first determine what it is that makes Final Fantasy, well, Final Fantasy.
For starters, be sure to include some FF-specific "markers", such as moogles, chocobos, and references to Ultimate beings (in whatever form) such as Ifrit, Shiva, and others.
Magic should be mana-based, like Psionics. Or, you can duplicate magic-like effects using superheroic powers like others have suggested.
Final Fantasy, to me, doesn't exactly mix fantasy and high-tech so much as having small areas of high-tech in an otherwise normal world. The further you get away from civilization, the less "tech" you see, just like in reality.
FF doesn't have a "religion" per se, although many games have had references to God and/or animism (worship of spirits). As such, the D&D cleric as is doesn't fit the bill; you'll need a much more open form of magic. You could still have White (Healing/Defense), Black (combat/elemental), Blue (duplicating monster skills), Time (Haste/Slow etc) or whatever divisions you feel like, but the arcane/divine motif no longer applies.
This goes into what "version" of FF feel you're looking for. The earlier games (pre-VII) focus on a most medieval/fantasy world with elements of super-high technology (ie airships, giant robots, and Magitek). VII and VIII are really the only two that "focus" on modern-day and beyond-type technology. X goes back and says the world used to be high-tech but wrecked itself and so you're back in fantasy-like conditions... but again with the high-tech elements sprinkled in (robots, bombs/grenades, the uber-airship etc).
IMO, D20 Modern and Urban Arcana might be the best bet for you if you want to simulate high-tech meets low-tech type stuff and want to stay loyal to the D&D mechanic. In fact, all Urban Arcana IS is D&D in modern times; it's not difficult at all to use one with the other with little to no changes at all.
Feel free to ask more questions if we're not touching on what you're looking for.
