For the last two years, I've been cutting back on tomatoes. So I've put carrots in the front half of a 8'x4' raised bed that was filled with the extremely sandy native surrounding soil of a low hill. I dug in some 10-10-10 fertilizer (just because that's what I had on hand) before seeding and sprinkled a little on top as well. I watered often during the season because the sand dries so fast and good carrots need consistent moisture. I am better at thinning than I used to be, and it does make a big difference. I was very pleased with the results.
I used to grow carrots in my front garden which is mostly clay, they did OK there too and less need to water. But I do think they were able to get bigger and longer in the sandy soil.