The one-of-a-kind F.P. Journe watch will be on display in New York before its sale in December. The director spent $120 million of his own money on the film, which grossed just $14.4 million.

Paul Boutros, the deputy chairman and head of Phillips Watches for North America, professed to have little idea what Mr. Coppola’s might fetch later this fall. But, according to Mr. Boutros, starting ...