Does anyone know how health coverage works if you live in Alsace but work in Switzerland? I've done lots of reading up on the French system, but it still isn't clear to me if we would be covered or we'll need to keep our Swiss health insurance.
I do have a number to call in Colmar, but my french is so bad, I'm afraid I'll misunderstand something and end up either not insured or doubly insured.

Complicated this one. I believe you will be covered by the "Secu", the French social security system, but most of my frontalier colleagues have complementary insurance allowing for treatment in Switzerland.
Your HR people should be able to give advice.

You do not need to keep your Swiss insurance but you will need to get a private insurance in France. There are many companies offering it, just google assurance frontalier Suisse. You can add the Swiss treatment option as well, which will of course increase the price - I think most insurances even without the option still cover treament in Switzerland if it is an emergency.

Thanks very much for both answers. Is the private insurance an extension of the french public one or is it a replacement? My husband and I both have CH citizenship and the laws always pertain to EU non EU, so I can't seem to find way the health system works for Swiss citizens. I've just tried Alptis insurance company, and they were lovely but my French is so bad I had to give up and say I'd call back

This article explains things in a bit more detail. There is a multitude of offers out there, but they are in French. A taste of what's to come, language-wise, if you live in France - the French don't really entertain the idea of communication in another language, even though in Alsace you can find the odd person who speaks local dialect in an office.

If you have Swiss privat health insurance, think twice whether you want to cancel it. If you want to get back in at any point, you may be considered a new risk, and you premiums (and exclusions) may be reassessed as of the point in time when you reapply = when you're older and are likely to have more pre-existing conditions.

It's a replacement, you do not need to pay into French public health care system. Sorry, don't know for sure either if there are any exceptions for Swiss citizens. Try some more companies, most of them have somebody able to speak German.

Ok, the next route is to try border towns for a german speaker! I'm slowly working my way through the link you posted tom.
@Tom Tulpe: We loved Offenburg btw, visited the schools, etc and the people are incredibly nice and the schools excellent. My husband just couldn't bring himself to be away for four days and with the kids for only 3.

Bear in mind that there is always the option to go with the Swiss system (KVS/LaMal). French frontaliers usually don't do that and opt for private insurance (usually) or the French social security (rarely), but most of these private policies allow treatment in Switzerland for emergencies only. If your level of French means that you struggle to read that website, you should consider an option that allows you to be treated in Switzerland rather than having to get to grips with the French healthcare system in French.