As the name indicates, French Polynesia operates in certain respects under French law. France has an extradition treaty with the US. However, France and many other countries will not extradite people they determine to be wanted for ‘political’ reasons.
I am sorry, i should have added a sarcasm tag.
Having said that, breaking the law is breaking the law.
Pick up Obama! Make him an exile in French Territory like Roman Polanski. Can’t cause too much of a problem in French Polynesia.