Going by the French. You could very well just say "happy eid", but it's not as clear what you're referencing in English without context, and the holiday is generally known in English by the full "Eid ul-Fitr". Suggestions welcome on that point.
Eid ul-Fitr is the English spelling of a Muslim holiday. Actually, I noticed a mistake in my translation: I was unaware that there are multiple holidays known as "Eid". Because of the lack of knowledge of Muslim culture in America, this phrase is a bit awkward to translate; normally, we wouldn't just say "Happy Eid". Not sure what to do about this.