I'd suggest dropping Action Surge if you're going to be getting spells at 2nd level. Drop Action Surge, give them Arcane Smite (as the paladin, but let them make a one-time choice for the damage type, or maybe let them chose the damage type on a long rest). Drop the extra ASIs at 6th and 10th levels. Move Improved War Magic down to 15th level (the bard gets it at 14th) since Arcane Charge is of less value. Then just generally rearrange the abilities so they have the same "dead" levels as the paladin (9th, 13th, 17th).
Until they have war magic and improved war magic, their spells are likely to be less effective individually than just attacking. I tested War Magic once and found it actually deals more damage than the fighter's 2 and 3 attacks at certain levels, and otherwise it's pretty reasonably close. But without dropping a regular attack ontop of a spell (and even with it), they won't do evoker levels of damage. They'll be more resilient, though, and a better vessel for buffs, so it should balance out.
I've been wanting to redo the Warlock as an arcane half-caster, mostly because I'd like it to play nice with the multiclassing rules.