Private shools in France = catholic schools. I went to one. My parents didn't pay much more than in a state school (we paid a £300 p.a. 20 years ago as opposed to £100). Yes, however, education was better. But, as I understand it, the staff etc. are still paid by the Education Nationale, i.e. the state.
As for the UK, well, I will be deciding where I send my kids. If state schooling is poor, which it is in many areas, then I reserve the right to invest myself in my daugther's future, seeing as the UK is very liberal and has left it for me to decide to do so. Will she become a little pest? well that is also down, in part, to me at home and, with our respective origins and a strong belief in meritocraty, I think she will remain well grounded.