It depends on the terms of the license(s)
If the copyright owner has given exclusive rights to translate into French to all content it produces into French and then issues a license to a third party which allows them to also make a translation, then it has broken its contract with the translator. This would allow the translator to sue the owner for damages but it is unlikely that it would be able to stop a third-party. In general, a contract can only bind the parties subject to that contract.
If the third-party knew about the exclusive license with the translator the translator could sue them for tortious interference. If the third-party made the translation without permission of the copyright owner then that is, of course, copyright violation allowing the owner to sue and, if the terms of the license with the translator permit, the translator to sue in place of the owner.