The basic conflict relates to the bet: can Phileas Fogg travel the world in eighty days? Fogg is confident that he can, but it's by no means a sure thing, as he subsequently discovers. The world may have become a much smaller place, but Fogg still has to factor in all the various obstacles that can so easily hold up his travel plans. As well as the intrepid Inspector Fix of Scotland Yard being on his tail, Fogg finds himself hampered by his own sense of honor as a gentlemen and by his unshakable fidelity to what's right and wrong.
We see this on display when he bravely saves Princess Aouda from being chucked onto her late husband's funeral pyre. Fogg knows that, in addition to incurring the wrath of the local population, he could well end up delaying his journey and thus possibly lose the bet. But Fogg doesn't hesitate to do the right thing. He knows what's important in life, and the love that eventually grows between him and Aouda comes to mean so much more to him than the wager and its enormous prize.