train from Marseille to Monico?

The drive from Avignon to Marseille without traffic jams or time to put the car in the garage at the train station is just over an hour. The local train along the coast to Monaco takes 3 hours. Sometimes you have to change in Nice. You could simplify by taking the train from Avignon, either a local train or the TGV. Even the TGVs slow down after Marseille and go slowly along the coast. Assuming you are taking the train to enjoy the scenery, one thing to watch out for with the TGV is the reserved seats: you might be assigned seats on the lower level, on the side away from the coast, and facing backwards. Maybe a train expert can tell you how to get seats facing forward on the upper-deck if it's a double-deck train and on the coast side. The local train doesn't have reserved seats. If you just want to go to the coast, Cassis near Marseille, is a lovely place to visit and much closer. If you just want to get to the Riviera, driving is the fastest and easiest.

As Bets says, driving will be faster than taking the train. You can stick to the autoroutes (freeways) and stay well north of Marseille. According to viamichelin.com, the driving time without stopping will be just under three hours. Only you can decide if spending all that time on the road and paying tolls on the autoroutes will be worth it for just a day trip. I certainly wouldn't do it. I'll put in another vote for Cassis.

First thing - spell it correctly. Monaco. If you are in Avignon there is no reason to drive to Marseille to get a train to Monaco. There are frequent ones right from the Avignon TGV station. You are best routed avoiding Marseille because trains going through there change ends and those facing forwards are now facing backwards, etc. It is a dead end station. It will take 3:47 to 4:06 depending on which train, one way. From Marseille St Charles it will take 3:16 or 3:42 with one or two changes.