Praise be to Allah.
Questions of this sort are asked so often and by so many that it is time Muslims paid serious attention to their reformation in the light of the Quran and Sunnah (prophetic teachings), in order that such things do not occur in the first place. Special stress is to be placed on the lowering of the gaze, no bodily contact (including shaking hands) between men and women, wearing of the full hijab (women’s Islamic dress code), prohibition of meetings in secrecy in particular and of mixing of sexes in general, discouraging unwarranted travel to non-Muslim countries, and early marriages. As for the question about one who committed fornication, there can be two situations.
Either the man did it by force, that is, raped the woman. Such a man should pay her the amount of mahr (dower) in accordance with her social class, as compensation for what harm he caused her. As for himself, he should sincerely repent. And, if the matter has reached the authorities, then he should be punished according to the law of shari’ah (Islamic law). See Madarij. Or, he has had sex with a woman who consented to the act. There is nothing due from such a man except repentance. Neither the child is his, nor is the cost of upbringing born by him because it is an illegal child and must be attached to the mother and not the father.
The man’s marriage to the woman, for the sake of covering up the issue, is also not permissible. For Allah revealed in the Quran a verse whose meaning can be translated as: “An adulterer does not marry but an adulteress or mushrika (female polytheist). And an adulteress does not marry but an adulterer or mushrik (male polytheist).” (24:3)
It is also not permissible to marry a woman who is pregnant from an adulterous act, even if the man has fathered the baby in the womb, as it is also not permissible to marry a woman about whom it is not known if she is pregnant or not.
Nonetheless, if he repents, and she also repents, and she is not carrying a child, then it is permissible for him to marry her and begin a new life. If she is carrying a child, they must wait until she gives birth.
And Allah knows best.