Hayao Miyazaki is known for his fairy tale styled movies. They are not actual fairy tales, but they draw many elements from fairy tales. He also takes inspirations from modern fantasy authors.
I don't think there may be a popular folktale about a fish with human face. But there are several creatures in many cultures/gods that have fishes with human face and some of them are quite capable of creating violent storms and other sea disasters. Hayao Miyazaki may have taken inspirations from them. Examples of such creatures/gods are: Mermaids, Sea Nymphs, Water Sprites, Sirens, Dagon (god), Kappa (Japanese water spirit) etc.
Also the Disney DVD page says it is based on The Little Mermaid (may be a selling point).