Can the fulfillment of an ordinary person's prophecy about two people marrying be considered a "coincidence," and is it permissible to use the word "coincidence" or "luck" in this situation, and if not, what is the alternative?

What the man said might be an insight or based on circumstantial evidence. Using the word "coincidence" and similar terms is permissible if it is meant to signify that something happened by chance, without prior arrangement by people, while believing that everything is preordained by Allah. Sheikh Ibn Uthaymeen believes that using the word "coincidence" is acceptable, and that it is a common expression. Coincidence is used for humans because they do not know the unseen, whereas for Allah's actions, everything is known and preordained by Him. The evidence for its permissibility is what Muslim narrated from Anas (may Allah be pleased with him): "The Messenger of Allah (peace be upon him) went to Umm Ayman, and I went with him. She handed him a vessel containing a drink. He said: 'I do not know whether I happened upon him fasting, or he did not want it.'"