1 more dmg and effect dice is stronger than paying one less mana, I think that's too strong, he could have a ring just for elementalist that gives him that.
I think that is a good idea to give him arcane level 1 or (even level 2) and for that triple the costs for rest of spells, an elementalist also abandons his elemental spells.
As a bonus, he could look out for a level 1 spell of his favored element school that gets cantrip.
Or, before the game starts, he can tie a level 1 attack spell to his Mage, just as you bind a spell to a wand.
He is so good at casting this one attack spell, he can cast the spell like in sleep.