Whether or not you need a visa depends in part on whether you intend to stay for more or less than 90 days:
Stays up to 90 days - Americans can stay for 90 days without a visa. They may do so each 6 month period. For details, go here.
Stays beyond 90 days - If you are married to a French citizen, then (like me) you should qualify for a temporary residence permit (“carte de séjour”). It is awarded by the High Commission (“Haut Commissariat”) in Pape'ete. Go here to learn how to apply. If you are not married to a French citizen, go here to learn how to apply for a long-term visa.
According to the main entity responsible for promoting tourism in French Polynesia, Tahiti Tourisme, U.S. citizens must have a passport valid for a minimum of three months after the return date.