Fairy tale is compound noun, made up of two separate nouns. As is always the case with compound nouns, the first is singular and invariable, while the second behaves as a 'normal' noun, and can be plural if necessary. For example, 'This is a book of traditional fairy tales'.
It can sometimes be one word or hyphenated when used as an adjective e.g. 'a fairytale castle' or 'a fairytale romance.'