The information we are presented with is minimal. This is perfectly understandable but it means that no one in this thread has anything like enough detail or context to make any judgement on firing someone.
What if the man was simply making a pass at someone he liked but unfortunately was clumsy and inept at doing so? Should it never be possible for a man to ask a woman from work out on a date? What if the woman has a reputation of being a social justice warrior that hates men and loves any excuse to complain about any perceived slight. We have no idea on the ages or marital statuses of the two people. What if he is a married middle aged man with three kids and she is a young intern? That makes it sound a lot more creepy. What if they are both single and the same age and seem to have the same hobbies? Does that change things a little? You cannot judge this scenario based on a couple of sentences from the OP.
My point is not to defend him, I have no idea if he is a predatory creep or a good guy that made a simple mistake. But then neither does anyone else here. Get a lawyer so you can follow a sensible policy of sitting down with the accused and ask about his side of the story. Depending on the response determines your next action.