Is a child born to a Christian mother and a Muslim father illegitimate, given that the marriage contract is invalid and the mother is considered a polytheist?

If the marriage between a Muslim man and a Kitabiyyah (a woman of the People of the Book) is concluded with all its conditions and pillars fulfilled, then it is a valid marriage from which its effects arise. Among these effects is the legitimacy of the child's lineage, so he is not considered a child of zina (fornication/adultery).