No, Wicca doesn't use any special language, this is because magick doesn't have a language. We don't even need to speak to us magick. We can use body language if we wish, or just simply think about it.
Not language, per say, but some terms may be new. Astral projection, thought forms, moon phases, blessed be, merry meet, merry part, ether body; to name a few. But other than that, nope. Just use what you know.
It would usually still be in the Wiccan's native language, though.
And then there's jargon, which you would get in any specialization. Just like lawyers learn specialized language that is still technically their native language (or Latin), or doctors have specialized language that is still technically their native language (or Graeco-Latin), or people in a religion have special words for holidays or religious observances but it doesn't technically become a whole 'nother language...it's just jargon.
Latin is also the language of lawyers, many scientists, perhaps some Roman reconstructionists, and...well, Catholics, also...many traditional prayers are also given to some Catholic school children to memorize in the original Latin (my mother was one of them.)