health insurance (Paris)

Hi everyone, I have been living in Paris for nearly 4 years now and as my daughter has finished studying and commenced work she is no longer covered under my health insurance cover with GMC. She has a Carte Vitale but I would like to know peoples thoughts on their experiences with public health. Is it better to take out extra private cover (ie doctor, dentist, hospital, ambulance etc) and if so can anyone recommend a good company that has their cover details and contract available in English;

Thanks All