In the US the biggest risk is that you are injured while working, so having medical insurance is the most important. Presumably you, unlike we in the US, have a universal government-funded program to provide minimal help. Also, in the US if you covered a public safety subject up close, you would probably be required to sign a waiver of liability (so the subject would not be responsible for your injuries or damage to your property – ie equipment). Here, though, the subject also may require you to indemnify them should your own negligence result in damage or injury. To fund that you might need liability insurance.
All this may be different in France. I suggest you have a drink with a lawyer friend and talk it over with her/him, and you pick up the tab.