From the end of June or early July, humpback whales come up from Antarctica to breed and give birth in the waters surrounding Tahiti, Moorea, Rurutu, and Bora Bora. During late October or November, when the newborn calves are strong enough, humpback whales migrate back to Antarctica.
The peak season is between mid-August and late October. Consequently, if you want to see these majestic mammals, their amorous game, and the newborns, then this is the time to come. Some agencies offer excursions with professionally trained guides with proper behavior to ensure the marine mammals are respected and not bothered. If the weather is nice, and the whales are in a resting phase, you can even snorkel with them.