Praise be to Allah.
In order for marriage to be valid, it is stipulated that the marriage contract be done by the woman’s guardian or his deputy, because the Prophet (blessings and peace of Allah be upon him) said: “There is no marriage except with a guardian.” Narrated by Abu Dawood (2085), at-Tirmidhi (1101) and Ibn Maajah (1881), from the hadith of Abu Moosaa al-Ash‘ari; classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
And the Prophet (blessings and peace of Allah be upon him) said: “Any woman who gets married without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid… And if they differ, then the ruler is the guardian of the one who has no guardian.” Narrated by Ahmad (24417), Abu Daawood (2083) and at-Tirmidhi (1102); classed as saheeh by al-Albaani in Saheeh al-Jaami‘ (no. 2709).
If this woman does not have a Muslim guardian among her own male relatives (on the father’s side), then the Muslim judge should do the marriage contract for her, because the Prophet (blessings and peace of Allah be upon him) said in the hadith: “And if they differ, then the ruler is the guardian of the one who has no guardian.”
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: As for the woman who has no guardian, then if in the town or locality there is a representative of the ruler, he may do the marriage contract for her, or that may be done by the emir (chief) of the Bedouin, or the head of the village. If there is among them a leader who is in a position of authority, then he may also do the marriage contract for her, with her permission.
End quote from Majmoo‘ al-Fataawa (32/35)
Islam has given the guardian authority over marriage because of his compassion for the woman and his concern for her best interests. This is apparent in the case of the father, grandfather, brother and other male relatives of the woman who are concerned about her best interests. If she has no such relatives, then the ruler and the judge who take care of the interests of the Muslims, so guardianship is given to them, and not to individuals who may not care about the woman’s interests or who may give their own interests precedence over hers, especially if an individual takes over her guardianship so that he may marry her to himself.
Based on that, you erred by taking on the guardianship of this woman, because there are Muslim judges in your country; therefore you have to repeat the marriage contract.
If the judges in your country follow the view of those scholars who say that it is valid for a woman to do her own marriage contract, then in order to be on the safe side, for yourself and for her, you should appoint a Muslim man as her guardian, then he can give her to you in marriage.
The woman’s guardian can marry her, if she consents to that.
See the answer to question no. 104662 for more information on the format of the marriage contract in that case.
And Allah knows best.