fly United through SFO to PPT. Then take the Air Tahiti puddle jumper.
We flew Air Tahiti Nui last fall to Bora Bora for a sailing trip and it was a mess. Delayed both ways, lost bags both ways. Ancient Air France planes with ash trays still in the seats. Delayed 36+ hours coming back into LAX. Just a total nightmare. If you can do the Air France flights maybe worth it from LAX. Or consider Hawaiian Airlines flies from HNL. Might be worth looking at as well.