They had a crushing case of war-weariness, they only made a supreme but half-hearted effort during the 100 Days for their beloved hyper-charismatic emperor: here they would have to fight under a widely loathed regime for Austrian and British concerns, very hardly a popular cause with the French people at large, despite what Talleyrand may say behind closed doors about the balance of power. Besides, even if Nappy is dead, at this point France is massively simmering with rebelliousness, because of the hyper-unpopular Bourbon attempts to put the clock back to 1789. There are very good reasons why Nappy was able to pull his ride back to power single-handedly, besides his personal charisma, France had discovered that the Bourbon comeback were a way worse deal than Napoleon. Such a widely unpopular war for the sake of hated yesterday enemies looks like the perfect spark to unleash a successful Liberal-Bonapartist Revolution in France, even if Nappy is dead. If it won't be the 100 Days, it shall be 1830.
Don't just look to abstract concerns about the balance of power, look at the real internal politics of the powers involved.
Prussia has reformed his land forces too, to even greater effect, Austria shall fight them and the huge Russian armies Susano talked about, good luck with the two-front war and French aid is not really coming, they are busy kicking out Louis XVIII.
He may try to explain the anti-Bourbon rebels on the barricades why war-weary France needs to spill its blood for the Habsburg. I hope he takes a bullet.