When we say "high," we mean high vocabulary. Another word that comes to mind is snooty. Jules Verne isn't one to use two words when fifty will do, and he does it with all the flair of a Victorian gentleman.
Verne uses difficult and outdated words so much that we're forced to tie a dictionary to the hand we aren't holding the book with. But the point isn't just that he's an author writing during a specific time period (when a large vocabulary proved how smart you were). It's the language of a gentleman—an intelligent one at that. So we think the style works well for Phileas Fogg's story. It's about a gentleman gambler, after all.
Still, Verne isn't against throwing in a comedic joke or a good old-fashioned rumble in for fun. When these scenes come up, such as Passepartout vaulting a somersault and breaking the planks of the dock in the process, or the English and American insults thrown by Phileas and Colonel Stamp, the gentleman vocabulary becomes sort of comedic.
During times of great stress for the characters, the wording becomes sparser and sentences get shorter. The Sioux raid, Aouda's daring rescue, and the Henrietta's survival of the hurricane all contain more intense, curt language. The flowery gentleman voice becomes one that invokes more suspense than a leisurely promenade through the city of Singapore.
In all, the writing style gives us the space to get to know our characters—stiff, starchy, or comedic as they may be—but also gives us some suspenseful scenes to keep us reading. Jules Verne would've been insulted if his novels had been a snooze-fest.