1. If you are permanently resident in France you must register for taxation purposes at your local hôtel des impôts.
2. If you do not do so then you cannot stay in France as a full time resident and when you come to sell your house it will be classified as a résidence sécondaire and you will have to pay taxes on the sale.
3. To qualify for health care you have to contribute to the state by working and paying cotisations. Otherwise you must provide your own private source. See here 4. If you avoid paying cotisations by travail noir then you risk fines and even prison sentences.
5. If you don't have a social security n° then your kids cannot qualify for free education after the age of 16.
6. Become part of the system and share its benefits. GET LEGAL!