This really depends on what you want from a Gish class.
More specifically, what do you want from it that isn't covered by:
Bladesinger
Blade/Valor Bard
Eldritch Knight
Paladin
Hexblade Warlock
or, honestly, multiclass mixes of above, or the above plus dips.
This is a bunch of "I cast spells and can use a sword" archetypes above with a variety of gear and weapon layouts and spell lists. Any "arcane blade" will end up overlapping a bunch with the above.
I mean, do you want all of the features of Eldritch Knight + all of the features of Bladesinger + Paladin smites + Hexblade like attribute subsitution? Or what subset do you want?
...
Arcane Knight
1/2 spell caster (round up like artificer). Uses Sorcerer spell list.
d8 HD
Heavy armor, shields, all melee weapons, simple ranged weapons
L1: Spellcasting. Int based. Uses spellbook.
L1: Spellblade. When you cast an AK spell with a level, your weapon gains a bonus to damage equal to the level of the spell slot used. Damage type is (choose from list). If damage type matches, double bonus. This lasts for 10 minutes, or until you use this feature again.
L1: Subclass
L2: Can end Spellblade effect for extra damage or protection.
L3: Subclass feature
L4: ASI
L5: Bladesinger style extra attack
L6: Feature that modifies spellcasting. Imbue items with spells?
L7: Defensive feature
L8: ASI
L9: Subclass feature
L10: Utility feature (extra attunement slot?)
L11: Attack+Spell feature (like EK7ish), or automatic quicken spell?
L12: ASI
L13: Improved Spellblade (extra [W] maybe?)
L14: Subclass feature
L15: Defensive feature
L16: ASI
L17: Feature that modifies spellcasting
L18: Utility feature
L19: ASI
L20: Subclass feature
Or something like that?