Firstly, Fogg declares that it is possible to go around the world in 80 days at the Reform Club. He bets twenty thousand pounds against anyone that he will make the tour around the world in 80 days or less. What he does is indeed very risky as he could become a poor man if he loses the bet, hence a clear proof of him being a brave character.
Secondly, in his journey in the jungle of India, Fogg has to travel on the back of an elephant named Kiouni. Suddenly, his group meets a group of bandits who have kidnapped the daughter of a wealthy merchant. They decide to save Aouda by breaking down the walls of the hut where she is kept. He risks not only his life but also this might delay his journey and he does all that because of his bravery.
Thirdly, in a train journey to New York, it was suddenly attacked by a band of outlaws. When the passengers are later counted on the station platform of Kearney Fort, it is found that several passengers are missing, including Passerpartout. Fogg decides to go with the soldiers to save Passerpartout and other people. He has participated in another dangerous event which might get him killed. However, as a very courageous man, he did not hesitate to do all that.