What is the ruling of Islamic law regarding someone who swore an oath that something would happen, then doubted after swearing the oath whether it had happened, and immediately sought forgiveness? Is he obligated to fulfill his oath?

If you intentionally swore an oath that something happened, while you did not know its reality, this is a yamin ghamus (a perjurious oath), and it is one of the grave major sins for which there is no expiation according to the majority of scholars, except for repentance and seeking forgiveness. However, if you swore an oath believing that something happened, when in fact it did not, this falls under laghw al-yamin (a vain or unintentional oath), and there is no sin or expiation for it.