As a Permit G holder residing in France, you are in principle covered by Swiss health insurance, with a droit d'option if you are a Swiss or EU national:
• LAMal: Swiss compulsory health insurance — premium per person (« residents of France » tariff), coverage in both countries
• French health insurance (PUMa, often called « CMU ») — income-based contribution; cover in France, and in Switzerland for medically necessary care during a stay (EHIC) or planned care with authorisation
The choice is made within 3 months of starting work in Switzerland; without a choice, LAMal enrolment is automatic. It is irrevocable. See our detailed LAMal vs CMU comparison guide.
For other social security benefits:
• Family allowances: only one country has priority (Regulation 883/2004, art. 68) — Switzerland if you alone work, France if the other parent works in France and the children live there; the other country only pays a differential supplement if its amount is higher
• Unemployment: if you become fully unemployed, you are paid by France (France Travail), not Switzerland. Your Swiss employer pays Swiss unemployment insurance, but benefits are paid by the country of residence (EU Regulation 883/2004, Article 65)
• Retirement: you build rights in the Swiss system (AVS/LPP) for your periods of work in Switzerland, coordinated with any French rights