In principle, cross-border commuters residing abroad and their non-employed family members must belong to a Swiss health insurance fund. The insurance obligation starts with the beginning of the employment relationship and ends with the end of the employment relationship. There is a time limit of 3 months to join a health insurance fund.
Cross-border commuters from Austria, Germany, Italy and France can choose whether to take out health insurance in their country of residence or in Switzerland (option right). Cross-border commuters who do not wish to take out insurance in Switzerland must submit an application for exemption from compulsory insurance (for French nationals: "Choix du système d'assurance-maladie") to the competent authority in the canton of employment within 3 months of commencing employment.
Source: State Secretariat for Migration SEM, July 2021