how health insurance works if you live in france: https://en.comparis.ch/krankenkassen...nzgaenger.aspx
how to opt out of the swiss health insurance: https://en.comparis.ch/krankenkassen...gspflicht.aspx
specific for basel canton: http://www.kvg.org/en/exemption-_content---1--1036.html
apparently france is a special case:
Since 01 June 2014
French frontier workers have the possibility to apply their right to opt only for the French “sécurité sociale” or the legal health insurance (KVG) in Switzerland. The acquisition of a private health insurance is no longer accepted/allowed. The existing private insurance contracts may be continued until 31.05.2014. After that date the persons concerned have to insure themselves with the French “sécurité sociale” as well. Based on this revision of law, it is no longer possible to change into the Swiss health insurance system. This decision applies to all French frontier workers (incl. Swiss nationals).