It exacerbates the business cycle for very obvious reasons, and it also slows economic growth as it results in more conservative investment, and lower spending on the parts of both businesses and consumers alike.
The real world numbers seem to bear out that unemployment compensation of some sort is a good thing.
The real world numbers also seem to bear out that if an undue portion of that compensation must come from the former employer specifically, that it creates some unfortunate disincentives towards hiring in the first place, which reduce (or in extreme cases eliminate) the benefits.
In short, Patio1 is right in thinking that the French system has some drawbacks... but his claim that the French system is some sort of inevitable end result of worker rights is utter and complete rubbish. The problem is nothing to do with workers rights, and everything to do with the specific implementation.