Typically the airline will you happily check you in as long as a counter is open regardless of when your flight is leaving. If you were flying Lufthansa, you check in anytime since there is always a counter open. Unfortunately it looks like there is only one Korean flight from FRA per day, so you can't "piggy back" on an earlier flight.
Most international check in counters open 3-4 hours before departure, but it depends and is hard to predict. In some case (high status, premium class) they sometimes "sneak you in" early as a special service.
You can always check in online and get a mobile boarding pass (or print your own). If you don't have checked luggage, you can just go through customs and security anytime (on the same day). I did that on Tuesday from FRA (to the US) and didn't have to go to a check in counter at all.
See https://www.koreanair.com/global/en/offers-promotion/promotions-hidden/web-mobile-check-in.html and you can also ask the airline directly