The postal system in French Polynesia is generally quite efficient, and there are modern post offices on all the main islands.
Mail to Europe, the USA and Australia takes about a week. Postcards or letters weighing up to 20g cost 100 CFP to France, 140 CFP to anywhere else.
FedEx and DHL Express have offices in Pape’ete. If you need to send something fast from the outer islands, they can usually help out – although it will probably involve sending the item by freight on Air Tahiti.