Should I separate from my fiancée after someone claimed to be customarily married to her and spread rumors about her, despite my love for her and her denial of the incident?

This person is malicious and sinful; he exposed and defamed this girl, and he is a liar in his claim of offering advice. Spreading the matter is proof of his corrupt intention and his desire for schadenfreude and revenge. His action invalidates his integrity and associates him with the description of a transgressor (fasiq). His report should not be accepted except after verification, in accordance with the Almighty's saying: ﴿O YOU WHO HAVE BELIEVED, IF THERE COMES TO YOU A DISOBEDIENT PERSON WITH INFORMATION, INVESTIGATE, LEST YOU HARM A PEOPLE OUT OF IGNORANCE AND THEREAFTER REGRET WHAT YOU HAVE DONE.﴾ [Al-Hujurat: 6].

One must turn away from this man and his sayings, and advise him to fear Allah and cease slandering the girl. This is harming Muslims and seeking out their private matters, and it is among the gravest of sins.

As for marrying the girl, if her outward appearance is good and she possesses signs of religiosity, good character, and fear of Allah, then rely on Allah and complete the marriage. What has been rumored about her will not harm you, as long as it is not proven that she is still married to another man by a lawful marriage. And even if it were proven that there was an illicit relationship between them and she has repented from it, "The one who repents from a sin is like one who has no sin."