Why Is It Called 'MIDNIGHT'??

Then you've kind of answered your own question! :)

After entering a partnership with Barrymore's character, Colbert's character seems to be living an enchanted, Cinderella-at-the-ball life -- and then Ameche's character shows up and their little fiction is in danger of unraveling.

Of course, the Cinderella story has a happy ending after the unraveling.

"All you need to start an asylum is an empty room and the right kind of people."

I mistakenly thought that the train to Paris in the beginning of the film arrived at MIDNIGHT for the longest time!

Then I watched more closely and heard the titular line. Duh. Oh well, I still love this film just the same. Don Ameche is so hot in this film! Wow!

... first I thought that the movie might play just during one night, or until midnight - could also have been interesting.