An American, an Englishman, and a Frenchman walk into a bar… Yep, it's the start of a bad joke, to be sure. But Jules Verne doesn't use his characters' fatherlands to get us to the punch line—each character in the book is a symbol of his country's take on stereotypes and "manly" behavior.
Phileas Fogg is about as British as you can get. Verne lays it on thick, too, making Fogg ridiculously all things English: stodgy, stiff, unemotional, meticulous, intellectual, and methodical. It's almost as if he wrapped all the British aristocracy up into one character. We're almost expecting to see Fogg pull a teapot and crumpets out of his back pocket at any point in the novel. Verne continues to poke a bit of fun at the Brits through Fogg and his annoyingly "British" habits.
As a contrast, Passepartout is totally French. He's silly, cultured, down-to-earth, and appreciative of the arts. While Fogg is described as a "Byron," Passepartout is described as a "Moliere." Passepartout is highly emotional. He's a worrier, quick to anger, and also extremely passionate. He's really in touch with the emotional side of things and can see the romance blossoming between Aouda and Fogg when no one else can.
Colonel Stamp Proctor is almost a complete American stereotype. He's rowdy, rough around the edges, and completely illogical. With a red beard and a gigantic stature, he's like a legendary lumberjack come to life. But Stamp isn't the only American stereotype being made fun of here. Passepartout worries about the train being able to cross a rickety bridge, but upon being called a coward, he manages to suck it up—American-style:
"I afraid? Very well; I will show these people that a Frenchman can be as American as they!" (28.39)
Later in the book, Fogg takes control of a steamer by paying the crew to mutiny. Afterward, the captain of the ship tells him, "Captain Fogg, you've got something of the Yankee about you" (33.27). Americans: Crossing bridges and stealing ships like it ain't no thang.