Fae Language

An imaginary language, spoken by imaginary beings. Perfect.

Fae are, or at least believed to be, creatures different from us humans. They might look similar to us, but they are still alien to our world. And if they existed, then naturally they had equally as alien of a language.
Of course, learning different languages is no supernatural feat. It becomes much harder if you cannot find its native speakers, particularly so when those native speakers never existed in the first place. There are a few books on the topic, yet none of them seem to agree on anything. And many of the supposedly-Fae languages seem suspiciously similar to older forms of our own langugages.

Fae and humans

This is where things start to get confusing. In many tales involving fae, they only speak their own language - or languages. In others, fae are more akin to animals or spirits and seldom speak at all. Yet in many other stories, especially newer ones, the heroes can very well communicate with the Fae like it is no big thing.
How could we explain such a difference? Well, any number of reasons really. Fae Language could be a secret one, that does not in any way stop Fae from using our human words. Or maybe they bother to do so only with the most worthy one, making fun of everyone else. Finally, some storytellers might simply not know the lore very well - the prominence of Fae Language and human language in stories varies quite a bit between difference provinces.
Finally, there is the supernatural theory. The Fae Language is a language of power, giving certain control over the Fae if you know the right words. The good old "name is power", you know. So if someone was to learn the Fae Language they would not be truly human anymore, forever changed by that knowledge. In a way, studying the Fae Language would mean forfeiting your very soul.