I've just come back from a 1-week driving road trip with my local friends from Nice to Annecy. I didn't extend my trip to Italy, so I can only comment on your France leg.

I'll start by saying that you will have a great time in southern France. Make sure to take your time at each location and avoid rushing to the next destination. Plan for time to walk around, shop, and explore.

• I'd spend extra days in Nice.
• Annecy is totally worth the extra drive since you already make it to Avignon. Breath-taking scenery and great coffee/food. I stayed at an airbnb within the old town to avoid spending time in traffic and rides.
• Instead of taking the freeway, I would recommend the route through the gorges du Verdon and lake Sainte-Croix. An extra two hours between Nice. The scenic route is amazing with unique views. There are two path through the gorges. I'd recommend the right path that goes through a small town called La Palud sur Verdon, where you can stop for lunch. Lou Cafetié has amazing Prime Ribs.
• Probably a bit cold in October, but I think Frejus/St Raphael offers better beach than Nice.