Phileas Fogg has wagered he can circumnavigate the world in just 80 days, to successfully complete the game you must achieve this task. You are not allowed at any stage to backtrack, only forward journeys are permitted. Once you have left Paris you cannot return there. Also, if the only way to reach a given city is through Paris you will not be able to reach it during your current playthrough. The game is open-ended and there are multiple different ways for Phileas Fogg and Passepartout to end their journey around the world.
There are 196 cities on the map and each one will have at least one route onwards. There are various ways that routes can be found and includes conversing with other passengers during a trip, purchasing a time table in a city market, and exploring a city. Once you have found a route you will be able to select it to find out how much it costs. The higher the price, the longer and faster the route. Generally you will find the prices around the 230 pounds mark.