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In 1872 London, England, a newspaper headline reports the shocking news that the Bank of England has been robbed. When the fastidious Phileas Fogg arrives at the Reform Club, a private men's club, he complains that someone has already read his newspaper. Elsewhere in London, Fogg's former valet Foster goes to the employment office and quits. Foster complains to Roland Hesketh-Baggott, the recruiter, that working for a perfectionist like Fogg is torture. Overhearing their conversation, the unemployed Passepartout, a jack-of-all-trades, offers his services and is hired on the spot to replace Foster. After Passepartout meets with Fogg's approval, Fogg plays whist at the club, and discusses the robbery with other members. When they debate about how easily a criminal could hide anywhere in the world, Fogg theorizes that it would take only eighty days to travel around the world. Stewart, a club member, thinks the supposition preposterous and wagers 5,000 pounds that Fogg could not make the journey himself, with three other members joining in and raising the wager to 20,000 pounds. Fogg immediately accepts the challenge and, after finishing the game, returns home to fill a carpetbag with money and minimal provisions.
Fogg and Passepartout then embark on their trip, making Paris, France their first stop. There, Fogg consults with Gasse, the manager of the Thomas Cook travel store, who informs him that an avalanche has closed the route to Spain and recommends they travel by hot-air balloon. Undeterred, Fogg purchases the balloon, called "La Coquette," and after taking off in the airship, he and Passepartout sail over the French countryside. As they pass a mountain peak, Passepartout takes the opportunity to grab some snow with which to chill Fogg's champagne. At the Reform Club, meanwhile, the members read newspaper accounts about Fogg passing over the Maritime Alps.
After Passepartout is forced to climb the ropes and fix a broken gas valve, they are compelled to land in a town square in Spain. While waiting to meet Achmed Abdullah, who owns the fastest boat in the area, the travelers are entertained by flamenco dancers at a restaurant. When Passepartout joins the dancing with an impromptu performance, Abdullah agrees to loan Fogg his yacht, on the condition that Passepartout participate in the bullfights the next day. Although terrified, Passepartout follows the professional matadors into the ring and bravely confronts a bull, becoming a local hero when he survives the bout. In London, meanwhile, betting on Fogg's journey has grown into a national obsession. Lloyd's of London supervises the wagering, and later announces Fogg's arrival at the Suez Canal. There Passepartout has his first encounter with Inspector Fix of Scotland Yard, who is following them because he believes that Fogg is responsible for the bank robbery. After arranging with the British consulate to have Fogg arrested when he reaches Bombay, Fix poses as an agent for a steamship company and befriends Passepartout, hoping to get information about Fogg. However, the valet is only interested in discussing romance. Fogg continues to use his copious supply of cash to bribe the captain and chief engineer to speed the ship to Bombay ahead of schedule.
Upon landing, Fix discovers that a warrant for Fogg's arrest cannot be issued because the local consul has received no directive from London. After Passepartout angers a crowd by chasing a cow, he and Fogg board a train to reach Allahabad, but the train is forced to stop abruptly the next morning when the tracks end in the middle of a jungle. Fogg purchases an elephant, which carries him, Passepartout and Sir Francis Cromarty, another passenger, through the jungle. That night, they discover a Kali ritual during which Princess Aouda, the widow of a rajah, will be burned to death on a funeral pyre with her late husband. Determined to save the British-educated princess, Passepartout infiltrates the ceremony and impersonates the deceased. When the "body" appears to rise, the participants flee and Aouda escapes with Fogg, Passepartout and Sir Francis. Their adventure creates a scandal in England, where it is reported that Fogg and Passepartout were imprisoned for desecrating a temple, but posted bail and set sail for Hong Kong the next day. On the boat, Aouda plays whist with Fogg, and reveals that her never-consummated marriage was arranged.
The next day, Fix learns from a steward that Fogg plans to take a steamship from Hong Kong to Yokohama, Japan, and plots to arrest Fogg in Hong Kong. Upon arriving there, Fogg attempts to locate Aouda's uncle, but learns that he fled to Holland because of his illegal business practices. Aouda then accepts Fogg's invitation to continue the journey with him. However, Fix waylays Passepartout when he is buying steamship tickets and, after admitting his intention to arrest Fogg, drugs Passepartout's drink with opium. Fix then arranges for the unconscious Passepartout to be left in a small boat, hoping to detain Fogg. Passepartout's kidnappers flee when they hear a police whistle, and he awakens the next day aboard the steamship, having been taken there by police who found the tickets in his pocket. Passepartout is distraught when he learns his wallet is missing, and that Fogg is not onboard, but joins a circus in Yokohama to support himself.
The resourceful Fogg, meanwhile, has found alternate transportation to Yokohama, and finds Passepartout performing an acrobatic act. After being reunited, they leave Japan, and British newspapers later report that Fogg has arrived in the United States. The travelers stumble into a political campaign and parade in San Francisco, California, where Passepartout is drawn into a saloon when he spots some dancers inside. After Fogg comes in to find Passepartout, the beautiful saloon owner attempts to seduce him, but her jealous, knife-wielding bouncer warns Fogg to leave, and he and Aouda finally lure Passepartout outside. While Fix waits on the sidewalk, planning to join them on their transcontinental train ride, Fogg, inspired by the dangerous characters encountered in the saloon, sends Passepartout to purchase guns. When an electioneer named Colonel Proctor harasses Aouda, Fogg hits him on the head with his umbrella, then dodges Proctor's flying fist, which strikes Fox. Finally, with Passepartout equipped like a gunfighter, the travelers continue aboard a train, enjoying Western scenery, and witnessing a Native American peace-pipe ritual.
After safely crossing an unstable bridge over a gorge, Proctor insults Fogg during a game of whist and they challenge each other to a duel. However, their fight is precluded when the train is attacked by Sioux Indians, who kill the engineer and fireman. While Proctor and Fogg fight off Indians from inside the train, Passepartout is captured after he climbs up to the roof and jumps off to divert the tribe from the train. Later at Fort Kearney, Fogg rallies the cavalry to rescue Passepartout before he is burned at the stake. Refusing to wait a full day for the next train, the resilient travelers attach a large cloth advertisement to a wood railroad cart, which then sails them along the tracks like a ship. In England, the Reform Club members learn that Fogg and his friends have arrived in New York City and assume that he is on his way back to England. Carmichael, general manager of Lloyd's, and inspector Hunter of Scotland Yard, inform the club members that Fogg is the confirmed bank robber and will be arrested as soon as he steps foot on British soil. The members are further disappointed when they learn that Fogg has missed the boat to London and has boarded a ship bound for Venezuela, which has no British extradition treaty.
Unknown to them, Fogg has paid the captain to turn the steamship toward Great Britain. When they run out of coal, Fogg purchases the ship for cash, and then dismantles it to burn every available bit as fuel. As soon as they arrive in England, however, Fix arrests Fogg, thereby preventing him from meeting his deadline. Not long after, Fix returns to the jail to release Fogg, admitting that the real thief has been captured. A disconsolate and now impoverished Fogg returns to his London mansion, and secludes himself from Aouda and Passepartout. His spirits are soon restored when Aouda, who has fallen in love with Fogg, proposes marriage. He immediately sends Passepartout to get a reverend, and while he is out, Passepartout sees a newspaper and realizes that Fogg still has ten minutes to meet his deadline. Fogg at first dismisses as inconceivable the possibility that he made a mistake about the time, but then realizes that they had passed the International Dateline, and that Passepartout is correct. Fogg and Passepartout hurry to the club, but encounter more delays because of a hansom cab driver with hiccoughs and a reticent horse, and a charity worker praying for Fogg's sins. However, Fogg strolls into the club exactly on time, thereby winning the wager. The club members are quickly distracted, however, when Aouda enters the room, as no woman has ever been allowed on the premises. When she inquires about the rule banning women, Fogg explains that breaking the rule could spell the end of the British empire. Moments later, the normally flawless waiter drops his tray, a painting falls, and Ralph, a banker with Lloyd's, announces that this is the end.