Yes, the marriage of one of the partners, including to a third party, automatically terminates the Civil union (art. 515-7, al. 1 C. civ.). The civil registrar at the place of the ceremony must make a note of the marriage in the margin of the birth certificate (of the ex-partner who has married) and inform the civil registrar or notary who registered the original Civil union declaration (art. 515-7, para. 2 C. civ.). The latter then registers the dissolution of the Civil union and notifies both partners.
Please note: since January 1, 2007, a partner who marries a third party is no longer obliged to inform his or her partner in advance.