Francis Ford Coppola’s “Megalopolis” has been in the works for decades, but it feels like it is addressed to an incomprehensible future or a remote past. It landed at the Cannes Film Festival in May, and since then its word of mouth record has been mixed — at best. Half the vanity project of an attenuated magus and half the valedictory of a lion in winter, it reimagines New York as New Rome and comes alive in considering how empires die. 

“Megalopolis,” which cost $120 million to make and is likely to earn back a fraction of that, centers on a visionary architect who doubles as a prophet of urban renewal, Cesar Catilina (Adam Driver). Think Ayn Rand’s Howard Roark mixed with the activist Jane Jacobs. He dreams of a “perfect school-city” that reverses the concrete jungles planted by the likes of Robert Moses. His nemesis is the pragmatic mayor, Franklyn Cicero (Giancarlo Esposito). 

New Rome teems with character and incident. A television presenter named Wow Platinum is played with sexy absurdity by Aubrey Plaza. The mayor’s daughter Julia (Nathalie Emmanuel) begins as a privileged party girl before falling in love with Catilina and his blueprints. A banker of Muskian wealth is named appropriately, Hamilton Crassus III, and played by a superb Jon Voight. His degenerate nephew is a convincing Shia LaBeouf.

The loose inspiration for the plot is the Catilinarian conspiracy from 63 before the common era, a still-shadowy coup d’état against Rome’s consuls. The setting resembles New York City, but seen through a perspective possibly achieved by the historian Edward Gibbon after ingesting a tab of LSD. Catilina climbs in and out of a gleaming Chrysler Building, and the skyline is visibly Manhattan. At times, though, the setting dissolves altogether, resembling a bare stage or unfinished set design.      

Julia and Catilina’s passion and project mixes business and pleasure, but the movie’s most indelible affair is Mr. Coppola’s with the possibilities of the silver screen. Catilina recites Hamlet’s most famous soliloquy, and the camera grants the performance the intimacy of Shakespeare’s Globe Theatre. Hallucinatory sequences enchant like an Impressionist canvas recast in celluloid. A silver hand appears from a cluster of clouds and grabs the moon.

Catilina’s brainchild — for which he won a Nobel Prize — is Megalon, a miracle substance that could turn New Rome into a paradise. He can also stop time, and the movie’s tense as a whole is slippery, seemingly haunted by both the past and the future. We are a far way from the gorgeous classicism of “The Godfather,” Mr. Coppola’s long-ago masterpiece. Still, something of the mafia masterpiece’s interest in moral weightiness abides. 

Mr. Coppola does not hit every mark. When “Megalopolis” does not ravish it can bore, and its run time of more than two hours can test the patience of those accustomed to movies crafted with corporate precision rather than an auteur’s roving eye. Discourses on Marcus Aurelius and Ralph Waldo Emerson take the tone of stoned philosophy majors chatting in their dormitory. Who was going to tell Mr. Coppola, a living legend, “no”?

The movie insists that it is a “fable,” and at 85 years old Mr. Coppola, the seer of “Apocalypse Now,” flaunts his liberation from convention. Movies this weird hardly get made anymore, and even when they miss — and this one has no shortage of head scratchers — they are more satisfying than the social media-tested success of sequels and franchises. “Megalopolis” is unlikely to find a large audience or critical adulation. It’s ticketed for cult status.