Since I didn#t join you to SaFe, I'm totally forgotten (But I'm still sorry about the Porsche heating!)
All the times I've been there, I've used public transport (for just a 3€ you can use a bus up to Monaco!) But since you've got a car, I certainly would drive to Grasse (which I had done, if I'd been a female, too).
North of Aix is Gordes
, a spectacular perched village.
And Bargème (east-north-east of Aix, quite close to Cannes) is one of the most villages of France, a 'must', I think. But when you drive there, you should stop at Gonfaron before.
Since you've got a car and stay there some days, I suggest that you add Nice to your tour plan.
And might be, you'd like to go there a second time ... for doing a railway day tour
re "French food": you're in Provence ... and the food there is quite different to "French Food" - well, at least originally and still today in the non-tourism restaurants. It's really GOOD!!!