However, I’ll be guiding trail rides in the Swiss Alps this summer. I’ll be working for a french company as a contractor. The reason this company wants to hire me as a contractor is because I would apparently need to be a Swiss citizen to be able to work as an employee and be insured by them. Is this information correct?
No, that is not correct at all. You do not have to be a Swiss citizen to work for a French company. If you're French, they can employ you no problem. The Fench company's commercial liability insurance should cover your work activities outside of France as well.
But if you do a large part of your work in Switzerland, then the French company will have to organize Swiss social security for you, and deal with cross-border tax issues. That is probably why they prefer to get people who are already registered as self-employed in Switzerland, as that takes all the responsibilities off of their shoulders.
But in order for you to work as an independent contractor in Switzerland, you would have to be registered as self-employed in Switzerland. Basically that means opening your own company in Switzerland. There are a number of requirements which you have to meet in order to do that.
Being French can make it easier, as it is easier for French citizens to start a business in Switzerland, compared to people from many other countries.
You would need commercial third-party liability insurance. If you do register as self-employed in Switzerland, you can take out Swiss commercial third-party liability insurance for your company.
Whatever you do, do not simply show up and work on a freelance basis without registering as self-eymployed. That can get you into trouble.
It would be different if you got a job for a Swiss company. In that case, you as a French citizen could work in Switzerland for up to 3 months as a seasonal employee with minimal paperwork, and be covered by your Swiss employer's liability insurance.