You should be fine. Air Tahiti Nui's fare codes for award tickets are:

A = First Class

Z = Business Class

Q = Economy

If you are really worried about it, call Air Tahiti Nui directly. They'll reconfirm your itinerary for you and since you are traveling in a premium cabin will take your seat assignment request as well. You can find their contact information at:

http://www.airtahitinui-usa.com/company/offices.asp

Good Luck!