Upvote:2
There are multiple luggage storage services in Frankfurt airport including one that's open 24/7 and the service is reasonably priced. See https://www.frankfurt-airport.com/en/travel/transfer.detail.suffix.html/article/travel/luggage/storage.html
However, there are no services that would hold your bag and then check it in for you later. You will have to do this later yourself when the bag drop or check in counter is actually open.
You can store your luggage bag, rest a few hours and then retrieve your bag and drop it off later. In many cases you can enter and leave the secure area as often as you like. This depends a bit on what type of Visa/Citizenship you have. The only downside is that you will go through security and sometimes exit immigration each time you re-enter.
For more tips on how to spent the night in FRA see also https://www.airportsdata.net/gn/airport-FRA-accommodation/ and https://www.sleepinginairports.net/guides/frankfurt-airport-guide.htm