This seems like a question for the consolidator, AutoEurope. They should be able to tell you which rental company you will get your car from and where you can drop it closer to the French border if you need to do that.
If possible with your rental company, you could drop the car in Ventimiglia. There are 3 route options according to Rome2rio, from Alba to Ventimiglia. Then you could take the train across to the best rental town on the other side. The driving takes from 2.5 to 2.75 hours depending on the route you take. Click under "Drive," then on "Driving directions" to see the 3 options.
But you don't say where in France to want to go. That could be convenient if you are going to the Cote d'Azur. Not so much if you are headed farther north. Again, Rome2rio could give you a hint on the best routes if you put in the actual destination city. You also don't say what time of year you are going, so weather could be a factor.
Again, AutoEurope should be able to help you with this. Personally, we always used Gemut.com because of the great free downloadable brochure on car rental and driving in Europe and the personal service from Andy there. They are actually in Oregon. They work through AutoEurope, but somehow they have always been able to get cheaper rates for us than when we try to do it ourselves.