The marriage of a Christian man to a Muslim women is an invalid marriage. Allah says in the Qur’aan:
''And give not [Muslim women] in marriage to idolaters until they believe.” (Surah al- Baqarah: 221).
Therefore it is not allowed for a disbeliever to marry a Muslim woman. Allah also says,
'' They the Muslim women are not lawful for them [the disbelievers] nor are they [the disbelievers] lawful for them.” (Surah al- Mumtahana:10)
If he does marry her the marriage is invalid. The children are the children of fornication. They are to be given to the mother and ascribed to her alone – unless that was done out of ignorance concerning such law. For ignorant people the matter is different. In their case their marriage is still invalid. However, the children will be ascribed to the father since the act was done out of ignorance. That is, if he was ignorant of the law and she was also, the marriage is still invalid but the children will be ascribed to their parents due to their ignorance and there was some doubtful aspect to the intercourse. But if he knew the Islamic ruling and she knew the Islamic ruling and they wee being lax and disrespectful of the law of Allah, then the children are the children of fornication. They will be ascribed to their mother and will not be ascribed to their father at all.
The couple should be reprimanded and the penal punishment should be enforced upon him for having intercourse with Muslim women when he did not have the legal right to do so. This is what must be done if the Islamic state has the ability to do it. If he becomes muslim after that and Allah guides him, then he can marry her with a new contract.