It's not, but phonotactically, it's certainly going to take after the vowel as opposed to the ending /t/. French is not a phonetic language, as phonetic languages like Arabic says that each letter has a corresponding sound. Lettres muettes in French are a different case, and /t/s are generally silent towards the end. B, C, F, K, L, Q, and R are usually pronounced at the end of a word, while D, G, M, N, P, S, T, X, and Z are usually silent.
I dunno. I took French since the first grade, so that's what it sounds like to me in my head. I assume that they're going to go with the Japanese pronunciation for it, especially since the phonotactic nature of é is pretty much in the middle in terms of vowel placement in the mouth. Based on instinct, I'd generally end with the vowel as opposed to completely ending the word with a consonant since that's generally not how /t/s work in French. The only exceptions that I know of are: brut, ouest, huit, words ending with -ct ending, and words ending with -pt. Of course, my linguistic background's more in Latin, and I didn't study a ton of in-depth French outside of my first two years of undergrad.
Edit: I know why I feel that way. It's because of the word l'été ("summer"). If it didn't have the extra é at the end, I wouldn't pronounce the /t/ due to Optimality rules/phonology rules in my head. It's peculiar, because I can't recall off the top of my head a word that's even spelled that way right now. Actually, let me make a quick call to someone. He may be fluent in Quebecois French but it's French nonetheless.
Edit2: I made the call. And this dude's been speaking French since he was a baby and agreed. You cannot pronounce the /t/ at all because that's just not how the phonotactics work. He did think it was peculiar that it's [ét] because you just don't see that. Either way, that's not how French works. If it's CV, then you don't pronounce the ending consonant. If it's VCC, you do in some cases like -ct and -pt.
I'm surprised they didn't go with Musée, myself, but that might be because that word means "museum" in French. If they were to pronounce the /t/ at the end of the word, it would've been spelled "Musétte" instead.