After you identify a nice train schedule using DB, then it works better at RE to break up the trip into the separate chunks that require reservations and enter each one individually into the shopping cart, such as Venice-Milan, Milan-Nice, and Nice-Avignon (but not any regional, unreserved trains that sometimes appear in the mix).
Italian trains don't particularly limit the number of rail pass travelers on board, but the reserved French trains do. For April 14, it will be important to get the Nice-Avignon reservation online now, e.g. for the 16:04 departure, and I see that they are available, at least in 2nd class. Italian reservations can be purchased at a train station or travel agency there, if necessary.