This is near the top of my list. Seems to be a missing niche.
Names for the class and 2 subclasses
While not my first choice or favorite...and stripping directly from Pathfinder, but being this is homebrew it shouldn't really matter, I guess...
I'd go with base class: MAGUS.
The Fighters fight with her weapons. The Wizard fights with his spells. The Magus trains hard and long to fight with both, simultaneously and/or in synchronous harmony.
Then for subclass archetypes, you get....let's say "Studies."
Study of the Sword (so you end up with a "Swordmagus"
is the "base base" subclass. The basic, simplest, straight up fighter/mage guy.
Medium armor, no shields, simple weapons + (but not full on any/all martial weapons)
Half casting progression (which one will not for the Pally and Ranger, does NOT include cantrips), spell levels 1-5. With Spells Prepared (from one's spellbook).
Special abilities/features, off the top of my head, include [but not limited to]: the use of their primary weapon as an arcane focus; being able to use more spells as bonus actions or reactions[?]; some kind of disadvantage to target rolls against their spell save DC for certain spells/situations, etc...
Study of the Battle (so you get a "Battlemagus")
The more martial/heavy hitter of the crowd. Add in Heavy armor (still no shields). Add in all martial weapons.
Feature to include more "battlefield control" type magical advantages/disadvantages type stuff, use of rituals to cause or increase area effects; scrying/divination stuff, some paladiny auras' type stuff?, etc...
I would add in a third option at the get go...and move the Hexblade to here...who maybe is more "sorcerer" than "mage" with renewable Spells Known instead of Prepared?
Study of the Shadow (oooo, "shadowmagus." I like that...but we already have shadow monks and shadow warlocks...

Ok make Hexblade a 4th subclass)
More Roguey/stealthy than the other two options. More the "arcane magic-using scout" or infiltrator than the armored behemoth or the simple sword- mage. BUT -have to be careful- this might not be different enough from either shadow monks or shadowy/hexbladey warlocks to warrant a subclass...in which case, just make a Hexblade the third subclass.