They're not fruit flies, but fungus gnats. Isn't that a nasty name--it makes me cringe, though I've learned to live with them. They live in the soil, and thrive when the top layer is consistently moist. Letting the top inch dry completely, or putting a layer of gravel in can help, but it's really hard to completely get rid of them. I've never had plant damage from them, though I read that large infestations can cause root damage from grubs. I watch my watering and when needed use sticky traps-- you can get large ones to place on walks or hang, or small folded loop ones that go on a spike that you put in the pot.

You can put a layer of fine sand (butt can sand-Home Depot) on top of the soil. That will keep the adults from 1) laying eggs, 2) prevent the larvae from emerging to complete their mating/growth cycle. 1/2" should do it. OR, you can mix up some Bacillus thuringiensis subspecies Israelensis (BTI), for a soil soak that will kill the gnats in the larval stage without injuring the plant. When there's no more larvae, the Bt dies off after a bit.

Good luck with that, I did both because they were flying all around my computer screen, driving me "buggy"

I've recently read that sundews and other carnivorous plants living indoors can help deal with these gnats and fruit flies. It's a kind of fun way to use our plants and gardening interests to get rid of some of the bugs.