The best time to travel to and visit French Polynesia is between the months of June and August which is when the climate of French Polynesia is at its driest and the weather is balmy.
Other times of the year are okay to visit French Polynesia but the weather is not as nice so your trip to French Polynesia may not be as enjoyable.
So I would plan the trip between the months of June and August to get the best experience from your trip to French Polynesia.
However during those time it's a pretty busy time of year because more tourists are going there at that time because of the best weather but it's still a great time to visit French Polynesia.