Your description sounds like a straight Eldritch Knight rather then a fighter/wizard multiclass.

I'd replace Dual Wielder with War Caster because, as stated above, you need a free hand to cast spells with somatic or material component, and War Caster solves the somatic component problem.

Another thing to consider is that you won't be able to use a spellcasting focus if you don't multiclass in wizard tho, so you will have to keep a component pouch.