Now that I think about it, they're probably not love at first sight. Ariel just thinks he's hot and probably just gets really fascinated by him. It's more like a strong crush. Then when they meet, Eric just has a crush on her at first, than falls in love. IDK, they're really confusing. Because Eric has love at first SOUND with her, but when he actually meets her, he falls in love, doesn't have love at first sight....And I count that more than the loving because of her voice, because he's ready to forget that fantasy to be with the girl he fell in love with.

This describes their relationship perfectly in my opinion.

Well, I think Eric didn't love her at first sight. Maybe he strongly liked her at first sight, but she definitely felt in love immediately she saw him.

Eh. Ariel wasn't really in love at all. She was in love with the world above. It could have been any good-looking guy stood on that boat and she'd have gone arse over tit for him. It's more of a squee fangirl obsession than a love.
Eric sort of pitied her and liked her funny quirkiness. He gradually fell in love and she sort of went from "OMGZAHUMAN!" to "He's actually a really nice guy and my attraction is based on personality rather than species!"

Love at first sight is a misnomer. The term would be better used as lust at first sight. Seeing as there is no possibility of love without knowing at least the other party's name.

It seems what thier relationship is although, Eric has more falling in love whereas Ariel fell for him at first sight.