Unfortunately, there is no easy way. It's like asking for the "fast and easy way" from Telluride, CO to Sedona, AZ. And when you say "same day," what time that day do you need to be in Arles? It's a long trip, so you may need to leave the day before no matter what.
Using the Bahn.de website http://reiseauskunft.bahn.de/bin/query.exe/en, it shows that trains on that route take 11 to 12.5 hours, and involve 3 to 6 changes. There is no single overnight train, only a series of trains, so you won't get much sleep. To see your train options, follow Rick's tutorial: http://www.ricksteves.com/plan/tips/db_tips.htm
If you rent a car in Italy, you will have to pay a potentially substantial drop charge for returning it in France. However, split among 5 people, this may be the better option. Viamichelin http://www.viamichelin.com/ estimates 5h33 for the drive, at a cost of €114.20 (€52 in tolls, the rest in gas). Of course, that's on top of the cost of car rental, and the time you spend picking up and returning the car at each end. And you'll need a vehicle large enough for 5 people plus their luggage, which again will cost more.
Is there any way you can break up the trip? Say, stopping for the night in Nice?