If you work in France with your family, an allowance is paid after the birth of a second child and until the child is 20 years old: http://www.ambafrance-uk.org/Social-Security
State support is available following the end of a work contract in France. Unemployment payments are available following the termination of any contract, providing the period employment has been for at least four months: http://www.thelocal.fr/20130724/top-tips-if-you-end-up-jobless-in-france