I won't say it would be impossible to create a solid Red Mage job/Fencer class. However, it would be very difficult to balance against the other DPS classes. Given that the class would require heavier armor than any mage class and a rapier class weapon, it cannot easily fit the Healer role (though something like Physick would be good for survival purposes). Nor can it easily fit the Tank role (it never wore heavy armor and never had great defense).

Red Mage/Fencer would likely fit as a magic DPS, though in closer combat than Black Mage/Thaumaturge. En-spells would be a given for the class (as I'd suspect it would fit a Rune Fencer-type job in the future). An Adloquium/Phalanx ability would also be a given for the job, as would a Doublecast ability.