As defined by the French Code Civil, civil liability punishable by law happens when injury caused to a third party obliges the person responsible for said injury to make reparations. This must be undertaken whether the injury was caused by negligence or imprudence. Civil responsibility is also engaged when the action leading to said injury was caused by third parties for which one is responsible (children, animals...).
Insurance companies generally cover this risk in their offers, but some may reduce it to cover only the time spent in training.
As covered by the French Penal Code, penalties are imposed on those who commit infractions, even if no injury ensues.