Couple things I've noticed and think need to be improved, changes in bold

Manafication: Increase intelligence by 5%. Duration 12s

I've noticed that buff from manafication never fails to fall off within one second of casting Scorch. This buff should last at least until we can cast our strongest spell. Additionally this buff should apply to any skill we perform making it so that if can now also buff Fleche and Contre Sixte.

Jolt 2 : Deal unaspected damage with a potency of 270

In cases where you're especially unlucky on Verfire and Verstone procs you suffer a 20 potency loss on every hard cast spell. This will help to even out the damage output of the job.

Corps-a-Corps : Additional effect, increase strength by 4000. Duration 10s

This would make auto attacks while performing a melee combo on par with physical melee jobs.

Engagement : Delivers an attack with a potency of 200

There's no reason that in situations where you have to stay in melee range due to platform sizes or game mechanics that you should be penalized on damage output.

Enchanted Reprise : Deals unaspected damage with a potency of 270. Balance Gauge cost 3 Black Mana, 3 White Mana.

Honestly, not sure if this is the best fix for the skill, but Red Mage is desperately lacking in long-term movement abilities when compared to the other two casters. Actual movement phases, red mage has dual cast and swiftcast, and then nothing. As it is now, using the skill is a DPS loss, so it's better to not do any damage for the rest of the movement phase than to burn your mana on this skill. Increasing its potency and decreasing its gauge cost might make this a viable movement skill. OR if the damage potency to Jolt II is also implemented, the damage potency can remain at 250 and just eliminate the gauge cost entirely.