Translation of "Corroborate" in French

Your story doesn't corroborate what I've heard before.

Ton histoire ne concorde pas avec ce que j'ai entendu.

Ray was willing to corroborate Gary's story, but the police were still unconvinced that either of them were telling the truth.

Ray était prêt à corroborer l'histoire de Gary, mais la police n'était toujours pas convaincue que l'un d'eux dise la vérité.