Is a divorce that occurs for administrative purposes—to register the marriage in France—considered a revocable divorce, necessitating the waiting period, given the intention to take the wife back after renewing the documents?

The divorce that occurred is valid and enforceable according to Islamic law, even if its purpose was merely a formality, due to the Prophet's (peace be upon him) saying: "There are three matters which, whether done seriously or in jest, are considered valid: marriage, divorce, and emancipation." Since the divorce occurred before consummation with the wife, it is considered an irrevocable divorce (ṭalāq bā'in) that does not require an 'idda (waiting period), based on the Almighty's saying: "O you who have believed, when you marry believing women and then divorce them before you have touched them, then there is not for you any 'idda to count concerning them." However, if the divorce had occurred after consummation, it would have been a revocable divorce (ṭalāq raj'i) with an 'idda, and it would have been permissible to take her back during the 'idda without a new contract.