The director talks about his passion project, ‘Megalopolis,’ including reports of problems on set and how he paid for the film.

Adam Driver plays an embattled visionary in this giddily spectacular mashup of futuristic New York and ancient Rome, science fiction and political intrigue.

Mr. Coppola has spent $120 million on his new movie, “Megalopolis.” Most box office analysts predict that he’ll get far less in return.