The Fae are not beings that humans interact with very often from what I gather at least not intimately so few if any would know their language. Most if not all sources you are likely to find are based on fictional novels like Artemis Fowl that have fairy characters. I am not saying this is impossible assuming they exist of course, yet it will not be a simple search.
Language is indeed a tricky thing when it comes to things like the supernatural. Language by way of words and grammar have a lot less meaning because the bulk of communication tends to translate from a combination of emotion, thoughtform (IE: imagery) and intent/energy. This is why you can find references and callings in so many different languages from english and irish to celtic, Old saxon, and even fictional languages or ones developed by the individual practitioner through a personal gnosis.
The best thing to do is speak in your own language, and just speak in truth with clear intent and from the heart. As time goes on and as you befriend the fae around you, they may help give you a few words or terms you can use when dealing directly with them, if you ask. They will be words that carry a specific tone and vibration that is attuned to their energies.
To start off just try to find words, phrases, and patterns that help you feel a connection to fae and what they represent. For example speaking in a loose rhyme. Or using a fore formal but free spirited choice of words. (respectful but positive/happy) Maybe putting a bit of a song-like lilt to your voice as well if you are musically inclined.
For example instead of saying something like " I invite friendly fae into my garden" you might doll it up a bit. Something like "To all the joyous faefolk who wish to join me in my happy garden, I bid you welcome!"