Passenger pigeons only mate when they live in huge flocks. That's why conservation attempts at the U. of Chicago around 1900 failed. Humans would have to restore immense numbers of passenger pigeons and then they might get out of control. Charles C. Mann in 1491 called the vast flocks of the early 19th Century "pathological." The emergence of stupendous numbers of passenger pigeons probably was the result of European or Indian impact on the landscape in some fashion.
In other words, wooly mammoths!
This French possession is isolated and unpopulated but surprisingly large (over 2,000 square miles). The climate is appropriate for Ice Age beasts.