Note that if your plan is to travel Paris - Nuremberg in one day than that is what you should plan and book. There is no need to make a priori assumptions about the route, and to split the tickets.
If you go to www.bahn.com and look up times you will see that the fastest routing is via Stuttgart, not via Frankfurt. However via Frankfurt is all on ICE trains. Prices currently look good, and it will definitely be cheaper than flying. Book the whole trip on www.bahn.com
bahn.com is the official website of the German Railways. As this is a trip from France to Germany you can buy tickets either with the French Railways (SNCF) or the German Railways (Deutsche Bahn), but the German railways have more options here.
Flying to Nurenberg may be an option if there are direct flights. Flying to Frankfurt and taking the train from there will not be faster, only more expensive...