I feel a remake of FFV would be tricky because mechanically speaking, I feel FFV is fairly flawless outside of maybe trying to shoe-horn in some modern popular mechanics like maybe let Chemist class unlock crafting mechanics, which I would be opposed to cause the last thing FFV needs is more reasons for needless grinding. I would keep the optional dungeon and battle with Enuo from the GBA version. I would drop the four classes introduced in that one cause they are unbalanced, not as fun as they should have been, and many of them were basically stepping on the toes of other classes (Cannoneer/Chemist, Gladitoar/Knight/Samurai, Lich/Blue Mage) but instead I'd add in a few new classes just better balanced and have them be obtained in a more sensible way such as having them be attached to the Earth Crystal, but obtained in Galuf's world cause the shards got stuck in Krile or Galuf's clothing when it shattered.

Classes I thought would work:

Class Name: Machinist
Weapons: Guns
Equipment: Light Armor, Cloth Helmets, Rings, and Gauntlets
Command: Precision Shot
Innate: Riposte
Skills Taught:
Equip Guns - Self explanatory
Precision Shot - Fire an attack that either does normal damage or ignores enemy defense 1/16 odds
Scatter Shot - Use an attack that hits all enemies for half damage.
Riposte - Works like Hamedo/Strike First from Tactics where the character attacks before the enemy does. Only works on Physical Attacks.
Overview: I like the idea of the Cannoneer and some of the skills the Gladiator had, but felt they should be better balanced and not feeling like a dumb persons version of a job. Guns are powerful, but have lower accuracy like bows. Most guns will also inflict status effects ranging from Blind to Condemn for the Ultimate weapon. The class is not very strong in terms of stats, but has good damage potential and a skill set very useful for other classes.

Class Name: Gambler
Weapons: Knives, Dice, and Cards
Equipment: Robes, Rings, Cloth Helmets, cloth armor
Command: Slot
Innate: Gil Up
Skills Taught:
Slot - Summon a slot machine that does various effects depending on what is pulled.
Coin Flip - Either grant a status buff to the whole party or enemy
Sleight of Hand - Casts a random Status Ailment on all enemies.
Gil Up - Doubles amount of Gil enemies drop, also raises item drop rate by 10%. Does not effect Steal rates.
Overview: Seeing how this class was originally developed for the FFV, it just seems fitting to have the class be put into the game proper. Class is about random chances and good fortune.

Class Name: Dark Knight
Weapons: Knightswords, Katana, Axes, and Hammers
Equipment: Heavy Armor, Heavy Helmets, Gauntlets
Command: Souleater
Innate: Reverse
Skills Taught:
Souleater - Sacrifice 25% of your health to do non-elemental damage to a group of enemies.
Reverse - Damage is reversed, enemy physical attacks heal the class while healing magic/item hurts them. Magic attacks works as normal.
Counter Magic - Innate skill that gives the user a 25% chance to counter cast a spell used on them. Can only Counter spells the user knows through other classes. Does include Blue Magic unless the spell in questions casts a status effect that prevents casting. Silence, Berserk, and Toad will negate the ability.
Overview: A favorite of mine, this class is a heavily offensive focus but is a bit of a glass cannon. Reverse gives them a chance to keep up their HP but also saddles with them with a lot of problems if you go up against a magic focus enemy. The real prize here is Counter Magic which will be super useful for Mime Mage builds.

Class Name: Onion Knight
Weapons: All
Equipment: All
Command: Onion Magic - All White and Black magic learned through their respective classes
Innate: None
Skills Taught:
XP UP - Doubles XP gains
AP UP - Doubles AP gained
Master Class - Grants an extra slot for all classes. Has a ridiculously high AP cost to earn like 2997 AP
Overview: This is the game's bragging rights class, it is earned once you unlock the Enuo dungeon, which in my mind will only be available after you beat the game once. The class is powerful with some great skills but few options. The class cannot equip Command Skills only innate ones like Doublehand or First Strike. As you've noticed, Onion Magic is exclusive to the class itself. The class has exclusive access to the Onion Gear which can be found throughout the game by doing certain sidequests or found in hidden treasures. These items have great stats and grants buffs like the Shield giving permanent Protect Status, Helmet giving Shell, and Armor giving Haste. So this class can be super powerful. The skills it does teach are great for endgame farming, and its final skill will open up a lot of new options for the gameplay.

Another thing I'd add to the game is a NG+ mode where you can restart the game back at starting levels, but carry over any mastered classes with you. NG+ will have altered enemies and bosses built for a tougher game. Beating that Mode opens up Fiesta Mode, where your party starts the game with only one class you choose at the beginning.