Praise be to Allah
The Muslims are unanimously agreed that it’s maybe not permissible for the Muslim girl to marry a non-Muslim, whether he’s Jewish, Christian or whatever else, because Allah, may He be exalted, says (interpretation associated with meaning):
“And give not (your daughters) in wedding to Al-Mushrikoon though he pleases you till they believe (in Allah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater, etc.), even. Those Al-Mushrikoon that is you towards the Fire, but Allah invites (you) to Paradise and Forgiveness by His allow, and makes their Ayat (proofs, evidences, verses, classes, indications, revelations, etc.) clear to mankind that they may remember”
“…then if you ascertain they are real believers, deliver them not back again to the disbelievers, they’re not legal (spouses) when it comes to disbelievers nor would be the disbelievers legal (husbands) for them”
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) stated: The Muslims are agreed that the non-Muslim cannot inherit from the Muslim, and a non-Muslim man cannot marry a Muslim woman.
End estimate from al-Fataawa al-Kubra (3/130).
More over, “Islam is always to prevail and is to not be prevailed over,” while the Prophet (blessings and comfort of Allah be upon him) stated.
Narrated by ad-Daaraqutni; classed as hasan by al-Albaani in Saheeh al-Jaami‘ (no. 2778)
The guy is with in a posture of leadership on the girl, which is maybe perhaps maybe not permissible for a non-Muslim to stay a situation of leadership over a Muslim girl, because Islam could be the religion that is true all the other religions are false.
Then she is a zaaniyah and is subject to the hadd punishment for zina if a Muslim woman marries a non-Muslim man, knowing the ruling thereon. Then she is excused, but they must be separated, with no need for talaaq (divorce), because the marriage is invalid in the first place if she was unaware of the ruling.