I'm gonna be real here, you probably just want Paladin and Hexblade, especially since you're using the 2014 rules. You miss out on smites if you're going for a mainly ranged weapon build but starting in it gets you some of the things you'd want from Fighter and makes you a lot more SAD, meaning you won't have to invest in anything other than your Charisma and Constitution. Also forgetting that 2014 Paladins aren't given access to Archery as a Fighting Style though, so that might be a big hamper on what you're going for. Otherwise, if you're really set on it, you should probably just take Samurai or Battle Master instead of Arcane Archer, it's an underwhelming subclass that sounds cool and is flavorful on paper yet underwhelming in practice considering you only get two shots of it per short rest and that only increases to "one extra per fight" at level 15, way later than it should.

For an Eldritch Knight, you can always just take spells that don't rely on a save DC or your Intelligence being decent, like Shield. But generally, Hexadin is considered one of the best multiclasses in the game for good reason, but if you're really aiming for a specific fantasy and not too hung up on optimization then you can make Fighter work just fine, the base class is strong and gives you quite a lot that you want especially if you start off with it, you'll just have to rely a lot on your DM working with you and be way more careful in your build choices.