Eldritch Knight is a fighter with a few spells, and I want a caster that fights, like a Valour bard without the singing or focus on skills. It also doesn't get the sort of spells a fighter would want; abjuration is pretty good but evocation is hit hard by the slow spell progression, it should have buffs that are good at any level.

I'm not sure that casting in melee is a big problem; an ability allowing it without disadvantage on attacks would be good for filling a dead level but there are plenty of spells with saves instead of attacks that don't have a problem in melee that could be cast instead.

I did forget about Extra Attack, yes. I was thinking one attack at sixth level, the same as the Valour bard.