Could be. Can go either way, really. The problem is that a Red Mage necessarily breaks current rules: you must give a DoM weaponskills or you give a DoW attack spells. Some people have suggested having weapon enchants as the spells, but that is not a Red Mage, that is a Mystic Knight.
Actually, come to think of it, Red Mage might not need to come from Fencer, but look otherwise to the Spellblade viera job in FF Tactics A2 and use THAT as a base class that can branch off into Mystic Knight as a tank or Red Mage for DPS.