Your miles can get you to French Polynesia (Papeete in Tahiti) from abroad but you can't use your miles to fly within those islands. I think they are only about 4 airlines flying domestically and none of them are part of any alliance.
It's not cheap to fly from one island to the other but if you want to go island hopping, your best affordable option is to buy an Airpass from Air Tahiti. Just don't carry too much luggage with you or they'll make you pay extra.

You can find here the current prices for Air Tahiti's Airpasses:
http://www.airtahiti.aero/articles.php?id=69