Sorry to perhaps disagree but maybe I misunderstand the question.

It should be no problem to check your bag in PEK through to ATL on the first ticket provided you take consecutive flights, i.e. don't have >24 hour stopovers. Same with ATL-CDG and CDG-FCO-FRA, maybe even ATL-CDG-FCO-FRA.

However, if you want to check your bag all the way from PEK through to FRA then it probably won't be possible. Are you really going to be taking 6 flights to get from PEK to FRA?