I'm not a fan of it. You get rid of the class's iconic spell combat and then try to balance it by giving them quicken spell at a level the class should not have access to. Even in most Final Fantasy games with the Red Mage, being able to cast two spells in a round is a capstone ability.
Bring back spell combat, scrap the bonus feat.
Charisma and Intelligence should be capitalized, as should all ability scores. Also, Charisma and Ibtelligence are ability scores - not "stats".
I'd scrap the bonus feat and early quicken spell arcana entirely.
You need to keep in mind that the FF job is really bland and doesn't have anything going for it other than being a fighter that can cast spells and having the ability to doublecast as a capstone. Except for having healing spells, these are things the magus can already do.
Here are your changes as I see them:
-Skill points change from 4 to 2, and a few skills change for flavor. This is fine because the class shifts its focus from Intelligence to Charisma.
-Magical abilities like spellcating, arcane pool, and magus arcana are governed by Charisma instead of Intelligence. The spell list was changed for flavor. Some spells were added, some were removed. You view the increased versatility as an overall loss in power.
-You reduce the size of the arcane pool and take away two magus arcana.
Without question this magus has been knocked down. I see no reason at all for the third change, especially if you feel that the modified spell list is more or less equal to the original one.
You have left something unanswered about the Cha-based spellcasting. Using Charisma strongly suggests that this is a spontaneous spellcaster, which brings up the following:
-You need a table of spells known.
-There is no spellbook.
-Spell recall, knowledge pool, improved spell recall, and greater spell access do not function as written. You can either modify them to function with spontaneous casting or simply replace them.
Wouldn't be easier to, instead of creating a custom spell list, to replace something like Spell Recall/Greater Spell Recall with the ability to learn a handful of spells from the bard list?
I think you should add some more abilities overall to give this archetype a stronger identity.
Also, if you've never seen it Here is the Red Mage as done by ffd20. Perhaps it could provide you inspiration?
I found that White Mage Arcanist archetype with 1 level of Swashbuckler and picking up the Eldritch Knight prestige class made for a superb Red Mage.
I think making it a base class is the complete opposite of what you want to do. Designing classes is really difficult and requires a very strong game mechanic and large scope to support it. The concept you have doesn't have enough to support an entire Pathfinder base class. The red mage just doesn't have enough there. And as Hark points out, most players might be better off just making an eldritch knight.