No, but you can leave it in a fee-based underground parking lot (the Cluse parking lot is the closest, 200 meters from the Children's Hospital).

You can also park in the Migros parking lot at Rue Dancet 21 or leave your car in a P+R parking lot (less expensive than the Cluse/Lombard parking lot), with the closest being the Bout-du-Monde parking lot (Route de Vessy 12).