And spark another war? What are you thinking? If that man really loved his son, he wouldn't have him wander all alone in some random mountain lost in the middle of nowhere.
Frisk just have to say "I'm really sorry, but I have seen no trace of him in the underground" or "He unfortunately was killed by the fall in the underground." It's alright to lie, Frisk. It no more serious than saying to Undyne that anime is real.