According to the bilateral Agreement with the EU do you need to have your basic insurance in the country you work in. If you wish to be insured for the basic insurace (KVG) in Switzerland, you should ask for exemption in France at the CPAM (Caisse Primaire Assurance Maladie) within the first three months. Additional insurance cover can be kept in Switzerland as you will live in Switzerland. All major insurance companies in Switzerland will be able to give you an offer for a crossborder cover.
In this case, you will have to make a decision quick, as you only have three months to get it all sorted, and believe me, the CPAM isn't quick.
More info can be found on www.kvg.org Gemeinsame Einrichtung KVG in Solothurn. Depending on were you live they will be your support and can advise you fully