Jules Verne did NOT include a balloon in his book Around the World in 80 Days, although, because of the movie, they think he did. (My first paperback copy of the book has a balloon on the cover).
Nevertheless, Verne DID use balloons in other books, and film adaptations have used the balloons as well:
The Mysterious Island (1961) the Harryhausen adaptation
20,000 Leagues Under the Sea (1916) – the silent film ambitiously attempted to include both 20,000 Leagues and The Mysterious Island at the same time. It also included great underwater photography (in 1916!), a submarine that faithfully resembled the one Verne described, and an Indian Prince Dakkar as Captain Nemo (the last time the character was so portrayed, AFAIK, until the graphic novel League of Extraordinary Gentlemen). Worth having a look at.
Five Weeks in a Balloon (1962) – Irwin Allen ,made it, so you know it’s not faithful, and they have a 1960s cast straight out of the adaptations-of-odd-books-cast-list (Red Buttons, Peter Lorre, Barbara Eden, Cedric Hardwicke, Fabian). And the Irish Rovers sing the theme song.
By the way, I don’t think balloons were used in any of the scenes except for long shots. Production photos show them using a basket suspended from a crane for both Mysterious Island and Five Weeks in a Balloon, and for Mysterious Island and 20,000 Leagues the long shots are clearly special effects shots. I guess real balloons are too unwieldy for real film production.