Is the marriage contract valid if the two witnesses are Muslim while the guardian and the one who wrote the contract are from the People of the Book?

For a marriage to be valid, the guardian (wali) of a Muslim woman must be Muslim. The guardianship of a disbeliever is not valid. As for writing the contract, it can be done by the husband or someone else, and the scribe is not required to be Muslim. Therefore, if the contract is concluded by the Muslim guardian of the Muslim woman, with the acceptance of the Muslim husband, and witnessed by two Muslim witnesses, then the contract is valid. However, if the woman's guardian is not Muslim, the contract is invalid, and it must be renewed by another Muslim guardian from among her rightful guardians taking charge of her marriage.