You need to decide if speed is more important or going along the Mediterranean is more important. The faster routes go away from the Med and back to it. We chose to stick to the water as much as possible. It took a bit longer both in the planning and the doing, but the views were well worth the time. Leaving from Sorrento, we weren't exactly on your schedule. We spent the night in Genoa and our final destination the next day was Antibes. You will need to decide where to stop for the night if you want to do that rather than spend 10 or more hours on the train.
For a first look, try the DB Bahn website: http://reiseauskunft.bahn.de/bin/query.exe/en. You cannot buy tickets there for Italy or France, but you can play with schedules, stopovers, etc. You can see the time it will take for the segments of your journey and how many train changes there are. You can see what kinds of trains there are. But best of all, after you choose a result to explore, you can click on a map that shows the route.
BTW, I did see that there is a TGV from Nice to Marseilles with connections to a regional train on into Aix. You might check to see if a TGV goes on to the Aix TGV station rather than the one downtown, but it is a good distance out of town and changing trains to go to the center might be a better option for you than taking a bus or taxi back into town.
I'm not sure where you've been looking, but Voyages-SCNF (http://en.voyages-sncf.com/en/?rfrr=reserver%20un%20billet%20resultatsheaderhome) is what I've used after checking things out on DB Bahn. Be sure to "uncheck" direct trains if you want to go to Aix center and put your ticket pickup country as France. Also be sure to put an early time in the morning to start the train listings. You can "arrow" over and back (following trains, previous trains) to see more trains and prices for that day. There seem to be some reasonable prices for the Nice to Aix part as an example, but they depend on the time of day you want to go.
Although the DB Bahn site will tell you if reservations are needed, the Italian and French ones will have the most information.