I'm making a High-Elf Fighter. An Arcane Archer to be specific (with some slight homebrew. Mainly just so I can use my Arcane Shot more). Due to picking High-Elf, I get a free cantrip from the Wizard spell list. Any good ideas? The character does have a high INT and my main weapons are a longbow, and a sabre (just a reskinned rapier that does slashing).

Given that you’ll be doing good damage at range with your bow anyway, I think your best option is a utility cantrip. Mage Hand is always fun, as is Message. Mending can be flavorful for recovering spent arrows and occasionally fixing something minor.

Any good ranged cantrip,is okay.Green flame blade and similar spells are good.Thunderwave and similar spells work best on martials.If homebrews allowed,I have good selection of martial designed cantrips.

I think having an attack cantrip that targets a specific save would be the route I'd take. Lot's of damage cantrips with secondary effects. A straight utility cantrip could be great as well, totally agree with pangurjan on that end of the spectrum. There are so many good ones in my opinion. Blade Ward since you don't want to get owned at melee range could be decent. Message sees a lot of use in my campaign. Ray of Frost to kite a target at range.

Just saw that Shocking Grasp could be another ridiculous kiting ability.OK, I'm done. So many possibilities.

Shocking Grasp?  I’ve thrown that on a High Elf EK Archer before.  If something gets too close in a fight, zap it and move to a safer position.

Between this and disengage, the down side is Shocking Grasp has a chance of failure.  Of course, the shared downside is both don’t prevent the baddie from just chasing you down.

Prestidigitation. Not for combat, but lots of fun use from it.  And no one will expect the fighter to make it look like the BBEG soiled itself.

Utility cantrips like Prestidigitation, or one that forces a save incase you really really just can’t beat their AC, preferably something that can do something besides just damage. But honestly, as a fighter, giving up all those attacks to cast a cantrip sucks.

Quote from HACRuzgofdi >>

Shocking Grasp?  I’ve thrown that on a High Elf EK Archer before.  If something gets too close in a fight, zap it and move to a safer position.

Between this and disengage, the down side is Shocking Grasp has a chance of failure.  Of course, the shared downside is both don’t prevent the baddie from just chasing you down.

 I was about to recommend the same thing for the same reason... 

Still, the cantrips that I think have the most potential for being major game changers would be Mending, Minor Illusion, or Mold Earth

I rather like Mind Silver, and the damage for it scales with your level.  It's verbal only, the range is 60 feet, but this is for when you can't use your arrows, so that's fine.  The damage is psychic, it is rare that anything is resistant or immune to that outside of Constructs, and has a side effect that messes with their next save on their turn.  You don't need to be the one who provokes the save, it can be anyone.  Their own save is based on Intelligence, and that's a score that is commonly dumped as well as a lot of monsters have a pretty low score in that.

Mold Earth sounds very useful for a ranged combatant.

I'll also recommend a utility cantrip since you already have range. Shape water can be really useful but really any of the utility cantrips will be a fun addition to your archer. 

If you like the idea of sniping/ambushing then Minor Illusion could be useful. You create a blockage like rocks, walls, thick brambles and you can hide in it firing arrows through it. Even if they look in your direction, they just see wall/etc and won't be able to see you crouched inside.

Get a portable hole and fill the bottom with something you could stand on and crouch, cover the top with minor illusion. Pop up, fire, crouch down. They'll figure it out eventually, but you could get multiple free shots before they do and when they do: you're at significant range so you have time to get up and move.

If you're not going that route, then prestidigitation or mending. 

I would either pick Dancing Lights for the ability to light up opponents who are 120’ away while staying hidden in the darkness or I’d pick either Sword Burst or Thunderclap so that when you end up in melee with multiple opponents you can potentially hit all of them with one spell.