Taking Caesar and Augustus for Rome would be like taking Reagan and Bush I. for America (for the sake of the argument only), they are just too near to each other and their civilization is practically the same. If you take however George Washington and Reagan, there are about 200 years between and you can represent America in two ways.
The same with Caesar and augustus, although they come from completely different ages (Pax Romana and Civil War), they are nevertheless one generation apart only. It would be much better to chose one of them and either one of the early republic, Marius or Scipio OR one of the later Roman Empire (like Marc Aurel, Hadrian or Diocletian, ...).
Germany: Frederick is more prussian, although he would be acceptable, we have plenty of other candidates throughout the Middle Ages, from the Ottons to the Salians and Welfs, there are many 'German Emperors'. (I translated these names into English based on my knowledge, it is possible that they have other names...) The biggest name screaming out is Friedrich Barbarossa, but nobody seems to answer my clam!
France: As I have said before, Charlemagne represents the Frankish or Carolingian civilization imo. He is one historical figure with lots of myths and as you say, could represent Germany as well (imo!). That's why the frenchest of all French rulers has to be there first, Louis "l'état, c'est moi" XIV.
mfG m