There currently is one option to travel by night train from Paris (France) to Nice (France), taking between approximately 12 and 13 hours: Namely the INTERCITES DE NUIT n° 5781 operated by SNCF.
The National Company of the French Railways (SNCF) operates a handful of lines throughout continental France.
In their night trains, they typically offer two types of carriages: seats and couchettes, with the latter available in first and second class.
The couchette carriages offer space for up to four people per compartment in first class and six people in second class. The berths are simply designed in both classes and are about 1.9 meters long.
Yes, it's possible to reserve an entire couchette compartment as a private compartment. This can also be done for a group.
The main difference is in occupancy: four people per compartment in first class versus six in second class. Additionally, first class berths are slightly wider. First class passengers have access to showers at stations in Paris and Toulouse. Second class offers bicycle transport for 10 euros, which may interest cycling tourists.
You should bring your own food as there is no restaurant on board. Alternatively, you can pre-order meals and drinks or eat before departure. First class travelers receive a small breakfast. Each passenger receives a night kit with refreshing towelette, dental cleaning tablet, sleep mask, earplugs, and water.