How do we turn it from a "you are use a sword and magic" into a story?
Wizard story: "you collect and find magic and study it".
Rogue story is subclass based.
Paladin has a story.
Barbarian has a (default) story.
Ranger, Druid, Cleric all have stories.
Monk, Warlock, Sorcerer all have stories.
Bard, Artificer has a story.
Fighter is a big light on story (even with subclasses). "You know how to fight" and "here is how you fight".
Do we go Rogue, and attach the story to subclasses? Make the base class something like "Spellguard" -- you use magic with weapons.
Spellguard -- Exemplar (1/3 paladin, you are specialist trained by an order to execute their will.)
Spellguard -- Bodyguard (1/3 fighter, you where trained in arcane magic to protect someone.)
Spellguard -- Bounty Hunter (1/3 ranger, you are an expert at tracking down and capturing people.)
Spellguard -- Cursed (1/3 warlock, your magic comes from your cursed blade.)
Spellguard -- Dancer (1/3 bard, you are a trained entertainer with magic.)
that is a possible framework.
Make it a 1/2 caster, and fill the subclass with appropriate utility spells.
For a unique mechanic, allow it to learn a limited list of concentration spells to imbue its weapon with. Also, make a melee attack as part the action to cast a spell (including a cantrip); sort of like EK on steroids that way (but doesn't get the rest of the fighter chassis, like extra attacks at 11 and 20).