I don't think the French President has the power to do that without a vote in parliament, and as she controls something like 0.35% of parliament...
Well there also has to be political will to fight a civil war which is anything but certain. And with other nations throwing their support for the defecting side just to interfere things could turn very very nasty very fast. And of course the loyalty of the military cannot 100% be relied upon in such a situation, it would be a disaster to morale to have to fight your former comrades in arms.