Three routes of driving from Nice to Chamonix

Route 3 uses the Mont Blanc Tunnel, which has a toll of 52.30 EUR in addition to the other Autostrada tolls.

Route 2 is the most scenic but it is ambitious to drive it in a single day: you have very long stretches of mountain roads. I do not think you can do it.
Route 1 is a more realistic compromise, but from Digne, going via Gap and Briançon does not make sense if you go that way. You should go via the col de la Croix Haute and Grenoble instead. And even then, you are looking at an 8-hour drive.

I would go through Italy.
If the Tende tunnel works are completed when you are travelling (they are due for this year I believe), you could go that way to Cuneo then Torino.
Otherwise, just take the motorway via Savona, it is a beautiful drive.

Thanks for reply,balso
For N85,from Digne,going via Gap,Corps and Grenoble is more exciting.
Looking forward to your views and opinions, thanks!

For N85,from Digne,going via Gap,Corps and Grenoble is more exciting.

Honestly, the direct D1075 from Sisteron to Grenoble via Serres and Aspres is almost as scenic (especially north of Aspres) as the A51 + N85 via Gap and it is significantly faster (by about 30-45 minutes). The N85 from Grasse to Digne is already quite long and slow, and Nice to Chamonix in a day is a long drive, so the time saving of D1075 is useful in my opinion.

Thanks,balso
In your opinion,I think the best route as following,
Nice-Grasse-Castellane-Digne-Sisteron-Serres-Aspres-Col de la Croix-Haute-Grenoble-Albertville-Megève-Chamonix
If we plan a stop, please suggest where we stay for one night.

Yes, exactly, that's my recommended route if you drive in a single, long day. It is very doable, I have driven from Toulon, to Gap where I had to drop somebody off, then to Saint Gervais and finally Geneva last May, it was perfect.

If you plan a stop and drive in 2 days, my recommendation changes to the eastern route, open only from end May to October:
Day 1 Nice - col de la Bonnette - col de Vars - Briancon.
Day 2 Briançon - col du Galibier - motorway to Albertville - Megève - Chamonix

Thanks,balso
If we decide to drive along Route 3, i wonder if we stay for a night en route.
after we stay for 2 nights at Chamonix, we drive to Beaune and visit Geneva en route.Pls give us some suggestions about the route (Chamonix - Geneva - Beaune).

You could spend the night in Torino if you go through Italy. Or Aosta, a smaller town with some good Roman ruins.

Regarding Chamonix - Geneva - Beaune, I am not 100% sure you need to visit Geneva. It is a pretty city, do not get me wrong, but I find it a bit grey, and driving and parking there is not very convenient. You would need to be careful not to use any motorway in Switzerland as it requires the purchase of a ~40€ toll sticker.

I would much rather recommend Annecy instead. Chamonix - Annecy by the A40-A410 (other routes are much slower), park at the Courier garage.
Then Annecy-Beaune by the D1508 to the A40 (motorway, but beautiful in the first stretch), then on to the A6 for Beaune.

If you do end up visiting Geneva: you could decide to cross the Jura mountains on your way to Beaune. I have never driven the whole route, but parts of the D1005/N5 (which goes Gex-Champagnole-Poligny) are beautiful, and you end up on the A39 motorway near Poligny. If you only have one night in Beaune, do not do this, but if you have more time, why not. And do not do this from Annecy either, the detour is too long.

Balso, thank you for these very perfect advices.
In the final days of the itinerary, the driving we prefer to as following.
Beaune - Colmar - Reims - Paris
we pick up our car rental in Nice and drop it in Reims(the itinerary suggested by Rick Steves). I'm not sure an additional fee for one way rentals.
Your suggestions are very welcomed by us.

Best Regards,