If it started out as French press coffee, I would not be able to tell. In my experience, I don’t mind reheated good coffee at all.
Starting with coffee that has sat in a drip coffee maker carafe, on the burner, until it turned itself off, I doubt I could tell if it was microwaved, but it would almost certainly taste “burnt” to me. I can’t stand that taste. But the problem would not come from the microwaving.
ETA: I may sound like a coffee snob in some way, but it’s just that I don’t like coffee enough to drink bad coffee.