Using a worryingly large slug of hotel loyalty points, I've just booked a two night stay on Île des Pins in New Caledonia, which is often called l'île la plus proche du paradis (the island the closest to paradise!). At the very least I need to get from the airport to the hotel and back, but possibly I'll want to spend a few hours each day looking round part of the island. For that, I'll really need a car, so I can get to beaches like this one:

Normally when I want to hire a car, I check with a couple of the bigger companies, check with some of the brokers, and book what seems the best deal. Unfortunately, none of the major chains seem to have an office there, and all of the brokers keep trying to give me cars in Nouméa, on a different island!
Is it possible to hire a car on Ile de Pins? And if so, what's the process?