Phileas Fogg does not actually change much during the course of the novel. He starts out as a precise, very methodical man, wedded to etiquette and proper manners, and ends the novel without changing his habits or his outlook on life. However, beyond his mannerisms and character, he does in fact undergo one major change: he discovers that he is not fully happy until he falls in love. Before the trip, his life was lived in a spartan manner, with little excitement. This was his own doing; he had few adventurous yearnings, or at least did not make them public. However, his life would have continued and stopped at his death in much the same way; the trip, and his chivalry towards Aouda, shows him that his own life is meant to be shared, not lived in isolation.
"...we might have made the tour of the world in only seventy-eight days."
"No doubt," returned Mr. Fogg, "by not crossing India. But if I had not crossed India, I should not have saved Aouda; she would not have been my wife, and--"
Mr. Fogg quietly shut the door.
...a charming woman, who, strange as it may appear, made him the happiest of men!
(Verne, Around the World in 80 Days, gutenberg.org)
This is the change of Fogg's purpose in life, his ultimate goal; instead of simply living one day at a time, he now has someone with whom to share his life. He can work towards a happy future together, instead of a stolid present, the same until death. In fact, it can be said that even this change is the height of Fogg's essential romanticism; what trip around the world would be complete without finding true love? However, since this was not his actual or immediate goal, and simply a side-effect of his general tendency to meddle and take action, it can be seen as a change in his character.