Is it permissible to break off an engagement due to the fiancé discovering that his fiancée has friendships with young men online?

If what has settled in your mind about your fiancée is merely suspicion and conjecture, then it is not permissible for you to express it or rely upon it, because "suspicion is the falsest of speech," and Allah has forbidden it. However, if the matter is based on certainty with evidence, such as seeing or hearing, then you must distance yourself from this girl. There is no objection to advising her to repent. If she repents, then it is permissible to continue with the engagement; otherwise, distance yourself from her. It would have been better to choose a woman of religious commitment and good character from the beginning.