Is it permissible for the husband to request the annulment of the civil contract documented in a European country, and does the wife have the right to refuse that, especially if her refusal deprives the husband of a second marriage, knowing that this contract stipulates for the wife that which is other than what Allah has revealed in the event of divorce, and does not allow the husband to divorce his wife according to what our Lord has prescribed?

The validity of a marriage lies in the Sharia (definition)-compliant contract that fulfills its conditions and pillars. Documenting it with official authorities is not a condition for its validity, but rather for safeguarding rights. A civil contract that prohibits polygamy or makes divorce contingent on a judge's ruling is invalid because it contradicts Sharia. If a civil contract prevents a second marriage, it is permissible to annul it, provided the marriage is documented in another way; otherwise, the wife has the right to refuse the annulment.