As an American living in Germany and working in Switzerland, I can address some of these:
As an EU citizen you can get a work permit in Switzerland. But there's a priority system for employment in Switzerland:
- Swiss citizens
- EU citizens
- Other citizens
The company that employs you has to be able to show evidence that they couldn't find a Swiss citizen for the job in order to hire an EU citizen. (In my case as an American, they had to show they couldn't find a Swiss citizen or an EU citizen. Luckily the job I applied for had been open for some 9 months.)
You will pay a small amount of tax in Switzerland, and a larger amount in France. The Swiss tax is automatically withheld. You are responsible for paying the French tax. In Germany I get a document every year from the German tax office showing me how much I need to pay each quarter.
Social contributions and insurance
My understanding in these areas is vague. As a cross-border commuter, I need to have Swiss health insurance (there are agreements with German insurance companies that make this not too expensive) and I also need to have Swiss accident insurance (which I've used in the last few months due to a cycling injury). As a 100% remote worker it wouldn't make sense for you to need these things, but that's not the same as saying you don't need them. You should check.
The accident insurance applies even if you don't live in Switzerland, and even if the accident doesn't occur there (though in my case it did). You can be treated anywhere, but if you're not treated in Switzerland, you'll generally need to show your normal (French) health insurance card and then either you'll need to submit claims manually to the accident insurance, or possibly they and the French insurance will be able to work it out without your input if you tell the accident insurance company the details.
Also withdrawn from my paycheck is payment into the Swiss retirement system, and I think it's likely this will apply to you even if you don't live in Switzerland.