Where did you see a train route from Frankfurt to Nice that goes through Switzerland and Milan?
Both Rome2rio and the DB Bahn search sites are showing the fastest routes through Paris with a total travel time of almost 11 hours and a transfer between 2 train stations in Paris. The trains shown are fast ICE and TGV trains. This would be my 2nd choice.
R2R shows total transportation time for flying at about 4 hours and 15 minutes, including to and from the airports by ground transportation. More than one airline flies this non-stop route. I don't think there's much chance for lost luggage. I think this is really the best choice.
R2R also shows that driving takes about as long as the train, and that is going the route you mentioned through Switzerland, Milan and Genoa . That doesn't count any stopping along the way, the cost of the vignette for Switzerland, tolls, the heavy cost of dropping the car in another country, etc. They do list the cost of fuel and an estimate of rental car cost.
I would not drive unless you would enjoy the driving and plan to keep the car to drive around France and then return it to Germany.