Only MileSAAver awards can be claimed on partners, including Air Tahiti Nui.
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"tn" should reveal what we might have - we do indeed have members who have flown between LAX and CDG on TN with award miles.
For starters, check
AA and Partner Airline Award info, rules (NOT for oneworld Explorer Awards) 2014
MileSAAver / SAAver Award Availability - Assistance & Discussion (consolidated) (where this query might be merged soon).
Be aware - since AA and US have not merged fleet nor policies yet, the American Airlines | AAdvantage (Pre-Merger) Forum is what you want for these current questions.