Hi Forbean, giving you directions depends very much on where you come from and where you want to go.
Reading you between the lines, I can only assume :
a - you work in Switzerland and reside outside of Switzerland, under the so-call « frontalier » status.
b - you want to (or already have) subscribe (d) to the swiss social security regime called « Lamal »
To make a long story short, before June 2014, a frontalier had three possibilities as far as medical insurance was concerned :
1 - adhere to the swiss system (Lamal)
2 - adhere to the french social security system
3 - adhere to a private insurance system
For 1 and 2, you could subscribe also to complementary coverage, with a private insurance company.
Since June 2014, option 3 is not any more an option. You have to choose between swiss Lamal and the french social security, called CMU.
Frontaliers previously under the private system (option) 3 do not have the choice to go to Lamal, they have to switch to the french social security.
There three cases where you can freely choose between french social security and Lamal :
1 - You are starting your work in Switzerland
2 - you are getting retired
3 - you restart working in Switzerland after paid unemployment period.
In case 3 (my case), I have been under french social security during unemployment, I have restarted working in Switzerland, subscribed to Helena, and now I have lost my job again, returning to pôle-emploi, hence being covered by french Social security, I am stopping my Helena contract.
Helsana is asking me to prove that I am covered by french SS since day 1 of unemployment.
I am still waiting the paperwork from CPAM, this is not a standard form yet.
As taki said, you cannot have a hole in your health insurance.
If you have a « hole » period, french SS is entitled to charge you at CMU rate, for the hole, plus continue to charge you if you were not entitled to choose Lamal.