I've always assumed it was a loan word from French, but I honestly also have never been properly able to figure out how to pronounce arbitrary words in French because I'm not familiar enough with the language. My perception is that the pronunciation for it is fairly regular, but I'd still need to take the time to learn it, and unless I actually spent the time to fully learn and practice French, I doubt I'd end up remembering the pronunciation rules anyways.

I thought it might be Greek, a language all Americans butcher constantly.

I think Gen Z will know the word bc one of the emotions in Pixar's Inside Out 2 was named Ennui and walked around with a French accent doing pretty much nothing :D