This article propose a new class for D&D 5th that tries to build a Fighter-Mage similar to the classical elf fighter-mage of AD&D 1st edition (or the elf of D&D Holmes or red-box).
In the new rules (excellent by the way) the most similar character to the Elf F/M is the Bard or some knowledge/magic version of the Cleric.
This class will be a very basic class, with few options since its versatility resides in spell selection.
This class will mix the feature of the Fighter with no martial archetype and that of the Wizard with no arcane tradition benefits, some features of both classes will be gained at later levels.
Hit Dice: 1d8 per Fighter-Mage level
Hit Points at 1st Level: 8 + your Constitution modifier
Hit Points at higher levels: 1d8 (or 6) + your Constitution modifier per Fighter-Mage level after first
Armor: medium and light armor
Weapons: simple weapons, martial weapons
Saving Throws: Strengh, Intelligence
Skills: choose two skills from either fighter or mage list
Roll that dice and keep gaming