The city of Nice has 3 stations, one nearby the airport, one near the former and new bus station, and a main one, Nice Ville.
Unless you are a regular visitor to Nice it is unlikely you will need either Nice Riquier or Nice St Augustine. Focus on Nice Ville. All trains, fast and slow, stop there. It is well linked to the Tram, and buses leave from there to the airport.
TGV trains from Paris and via Avignon TGV station head towards the sea and slow down as they wind through the seaside mountains, so the "Train of Great Speed" doesn't go all that fast between Avignon and Nice.
At Nice you change to the double decker regional PACA TER train which stops all stations from Cannes to Ventimiglia, Italy. Villefranche sur Mer is about 5 or 10 minutes from Nice Ville depending on if the train skips Riquier. Some trains do skip a few stations, and a few of the relief trains are made up of seriously ancient single decker carriages borrowed from Marseilles.
But most are the modern, airconditioned double deckers. Between Cannes and the Italian border, sitting upstairs on the right-hand side is very rewarding (as is sitting on the left on the return) because the line is mostly right along the sea - between tunnels - and the views are spectacular.
When the local train approaches your station, do not dawdle. The stations are often not announced so you need to know the order of the stations and should read the signs on the platforms as the train stops. You need to work the doors because they won't open unless you do. The train won't wait in the station very long, sometimes under a minute.
I find it surprising that a TGV would have the same number as a PACA TER. It is irrelevant though because the TERs are frequent. Don't forget to validate.
