Third party liability insurance (‘responsabilité civile’): it is a legal requirement for any kind of accommodation (and is not included in the rent). Sometimes the landlord will ask to see your certificate before you can move in. It’s not too expensive though - about 20 euros a year. The insurer will sell it separately, or as a bundle with normal household insurance.
Companies:
SMAPRI (from CEA when you sign your contract)
AXA (apartment &/or Supplementary Health insurance)