My spouse benefited from his partner's mutual insurance contract. The rupture of their Civil union was registered in Sept. , the mention on the birth certificates was made then. In the meantime, he'd an accident. Does he still benefit from the contract?

Yes. The termination of the Civil union only becomes opposable to third parties, here to the mutual insurance company, from the day when the publicity formalities have been completed, which means, from the mention made by the state civil officer on the birth certificates of the partners (art. 515-7, al.8 C. civ.).