Suggestions? Avoid France.
Not trying to be clever or funny but France is not a car friendly country anymore. My choice would be to go through Germany with side trips to Luxembourg, Mosel region and Nurburgring. Down to Stuttgart and the Porsche museum, then on to Zurich via Bodensee, heading then to Lugano , Lake Como, Genoa and Monaco
Just my thoughts
Sounds like a great trip. I did a similar one through entire France and arriving at the Cote d´Azur coming from the Camargue. Not sure though whether I would do it with the GT3 as in that case I would come and exit via the mountains indeed (and would want to cover the Col de Turini). You might consider the route Ian described above and which is pretty similar to Atz´ itinerary for his summer trip.
The drivers in France are OK but the police isn't. They love to give tickets to tourists and the more expensive the car...well...you get my point. I actually prefer the italian police...they are friendlier, interested in the actual car and if you play your cards right by apologizing and being friendly, you can sometimes talk you out of a ticket or at least lower the amount of it. I get stopped pretty often in Italy and this "strategy" always works...
The Austrian police is also pretty tough at times...they can guess your speed and if they don't like your nose...or your car...or both...well...
My wife started to hate South France: Too much traffic in summer (it took us five hours from Mandelieu to St. Tropez and three hours from Mandelieu to Monte Carlo), the food is not really good most of the time (unless you know your restaurants in the region) and there isn't really much to do for kids...unless you have a private beach and/or a yacht. Shopping can be pretty expensive, the variety and the prices are much better in Miami.
RC (Germany) - Rennteam Editor Porsche Panamera Turbo S (at Porsche right now), BMW X5M, Mercedes C63 AMG Coupe PP/DP, Mini Cooper S Countryman All4