Sure France wants the USA to do all the work. They would just be defeated by the Syrian army and have to raise yet ANOTHER white flag of surrender.
The French/British forces only need to defeat half of the Syrian Army—they would have the rebels on their side—and maybe the Turks. A no-fly zone could be imposed and the NATO forces could start to dismantle the Syrian Neo-Nazi Party in power. With a little luck they might get Russian support! I don’t think Obama will help in this fight.