I am 80% sure I saw the full acronym for FATE spelled out in-game somewhere the first time I played through Cross, and that I saw it either while going through the Dead Sea or through the Sea of Eden. However, I don't completely remember how exactly it was spelled out. "Future Altering Time Entity" may or may not be correct. Pouring over the "Full Game Script" submitted by Zeality on GameFAQs, I indeed cannot find any point at which the acronym is spelled out. I didn't actually pour line by line over the other CC faqs on GameFAQs to check for it there, but I did run quick text searches through all of them for "Future Altering Time Entity" with no success.
Still, I can't shake the feeling that the acronym is definitely spelled out somewhere in the game. Could it be that the Full Game Script is not completely complete? Does anyone else remember reading out the full name for the acronym? I can't get an emulator working on my current linux PC to verify...