Trenitalia and a private French rail company combined forces to create Thello (pronounced tell-OH), which operates overnight long-haul trains between Paris and Venice, with six stops in between. It is mandatory to travel with the appropiate international travel documentation a board this train.
Thello trains depart from Paris at 7:59pm and arrive the following day in Venice at 9:35am. Other stops in Italy are Milan (6am), Brescia (7:10am), Verona (7:54am), Vicenza (8:43am), and Padova (9:06am). In the other direction, Thello trains leave Venice at 7:20pm and arrive in Paris the following day at 9:30am.
There are both couchette compartments and sleeper cabins on Thello trains. Couchettes come in either 4-bunk or 6-bunk options, and sleeper cabins have 1-3 beds. The sleeper cabins are slightly more comfortable, with an en-suite wash basin and a bit more privacy. Couchettes are typically shared with other passengers, unless you're traveling with a larger group.
Each Thello train has a restaurant car, which all passengers are welcome to use, and of course you can have a DIY picnic in your compartment with French or Italian picnic supplies you bring along.