Wish is good . But the sentence itself sound unnatural. You should say ( I found out that you wish to travel to Paris ) or (I learned that you wish to travel to Paris . if you want to use wish take out the intend .

This sentence is not correct. It should be something like: "I've got to know why you wish to travel to Paris." or "I've got to know why you have intentions of traveling to Paris." You can't use both 'wish' and 'intentions', it sounds redundant.