Praise be to Allah.
In order for the marriage to be valid, it is stipulated that the marriage contract should be done by the woman’s guardian, and that it should be witnessed by two Muslim male witnesses, 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 Moosa al-Ash‘ari; classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
And he (blessings and peace of Allah be upon him) said: “There is no marriage except with a guardian and two witnesses of good character.” Narrated by al-Bayhaqi from the hadith of ‘Imraan and ‘Aa’ishah; classed as saheeh by al-Albaani in Saheeh al-Jaami‘, no. 7557.
The woman’s guardian is her father, then her father’s father, then her son (if she has one), then her full brother, then her brother through her father, then the son of her full brother, then the son of her brother through her father, then her paternal uncle, then his son, then the Muslim ruler.
If the woman is a Muslim, it is stipulated that her guardians should also be Muslim.
Ibn Qudaamah (may Allah have mercy on him) said:
With regard to a disbeliever, he has no guardianship over a Muslim woman under any circumstances, according to the consensus of the scholars, including Maalik, ash-Shaafa‘i, Abu ‘Ubayd and as-haab ar-ra’y. Ibn al-Mundhir said: Those scholars from whom we acquired knowledge unanimously agreed on this point.
End quote from al-Mughni (9/377)
Based on that, if your guardian is a Muslim, then the condition of having a guardian was fulfilled.
But if he was not Muslim, then the marriage contract is not valid, and must be repeated at the hands of your Muslim guardian, if you have one. If you do not have one, then the Muslim judge must do your marriage contract, if there is a Muslim judge; otherwise it may be done by the director of the Islamic centre or someone of similar standing among the Muslims. If no such person is available, then a Muslim man of good character may do your marriage contract.
With regard to witnesses, what is meant is that the marriage contract must be witnessed by two Muslim witnesses who are present at the marriage contract that is done between the guardian and the suitor. Everyone who is present at the marriage contract, such as a scribe, relative, official and so on is a witness to it, if he is fit to be a witness, i.e., he is a Muslim of good character.
Many of the scholars are of the view that if the marriage is publicised widely and announced, there is no need for there to be witnesses, because of the report narrated by Ahmad from ‘Abdullah ibn az-Zubayr (may Allah be pleased with him), according to which the Prophet (blessings and peace of Allah be upon him) said: “Publicise the marriage.” This hadith was classed as hasan by al-Albaani in Irwa’ al-Ghaleel no. 1993.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: Undoubtedly marriage that is publicised widely is valid, even if it is not witnessed by two witnesses. But if it is done in secret and with witnesses, this is something that is subject to further discussion.
If it is both witnessed and widely publicised, then there is no dispute that it is valid.
If there are no witnesses and it is not widely publicised, then it is invalid according to the majority of scholars, and if there is any differing opinion it is insignificant.
End quote from al-Ikhtiyaaraat al-Fiqhiyyah, p. 177
Based on that, if these two witnesses witnessed the marriage contract, or the marriage was widely publicised and announced, then your marriage is valid; if that was not the case, then you must do a new marriage contract.
And Allah knows best.