Hmmm... My Next Step for Final Fantasy. The series really has gone downhill since Square merged with Enix and half the original development team quit (FFX and beyond).
First off, I would go back over the old games and see what magic systems people liked the best, and what was the most effective. My own personal favorites are Magicite (FF6) and Materia (FF7) combined with spells at certain levels (FF4). None of these systems are overly complex or confusing, which is good. Perhaps a hybridization of all three has potential.
Tied into the Magic system is the Summons. Should only certain characters or classes/jobs (more on those later) be allowed to use summons, or should everybody? Should they Persist? Limiting it to certain characters or jobs allows for more character variety, while allowing every character to do it lets you use favorite characters rather than forcing a player to use a character for specific abilities.
Combat System. Oy... here's the big one. Personally, I think the classic FF combat system hit it's peak with FFX. That said, I would try to go for something similar to the Combat system of Chrono Trigger. No special screen if possible, moving enemies, ability and magic combos, and a smooth pace only marginally slowed for the bigger or longer spells and abilities. The ATB gauge can be replaced by the "who's next" window FFX had. Just try to keep it simple for players to learn by gradually introducing mechanics, but not SO gradually that you are still getting tutorials halfway through the game (I'm looking at you, FF13).
Pigeon-holing characters into only being able to use one type of weapon is terrible and it needs to stop. It leads to silly shit like looking for the latest model of combat glove or the Special Walking Stick Of The Gods. I mean, really guys? Every combat archetype or job needs at least two kinds of equip-able weapon, from Spiked Gauntlets to Cestus to claws to swords (there's LOTS of kinds of swords out there!) and knives, bows and crossbows to staves, rods and wands. Also, in this day and age, I don't think it's too much to ask that each weapon gets a different graphic or some kind of visual effect to go with it (Lightning Sword can look the same as a Longsword, just with arcs of electricity or sparks or something). The weapons and armor available can drastically effect character roles as well.
As for story and world... I'm all about exploring and side quests along with steady plot advancement. The ability to backtrack to certain or most areas is nice too. Fighting some gnarly monster on top of a mountain that you didn't necessarily NEED to climb for the extra awesome loot or Uber-spell is great.
Character development has gotten to be something of an issue for the FF series ever since Final Fantasy 7. Characters are getting more and more stereotypical (go cry emo kid, leave saving the world to somebody who gives a shit) and less engaging. People love Sabin and Edgar because they were interesting and funny. Locke was awesome because even though he had a tragic past and made mistakes, he didn't turn into a brooding pussy about it. Palom and Porom were good because thier chibi and loli wasn't pushed into your face in every dialog (and they save you from dying in the best manner ever). Alternatively, nobody gave a shit about Hope because he was constantly pushed in your face and utterly worthless for half the game. He went from a pity case to Real Damn Annoying very easily.
I'd go back to large open worlds full of spots to explore and check out. FF13's tunnel-vision gaming really... wasn't all that great for me. It showed a real lack of story-telling finesse, instead opting for railroading you into the story (such as it was).
So those are in my opinion the major fixes the FF series needs, or could benefit greatly from IMO, and where I would start.