brooke,
Nice would make a good stop in the south of France, especially as it's not hard to get from there to the Cinque Terre. The best way to get to those places would be via train. You can research the rail solutions on the Bahn.de (German rail) website, although you won't be able to buy tickets there for the trips you'll be taking. Note that you'll have to use the specific station names when researching, and will have to specify one of the five Cinque Terre towns as your destination. Do you have any idea which town you might want to stay in?
A few thoughts on each train trip....
- Dijon Ville to Nice Ville - one of the quickest routes appears to be a departure at 08:40, arriving at 16:06 (time 7H:26M, 2 changes - two of the trains are high speed TGV).
- Nice Ville to Monterosso - one of the easiest trips will be a departure at 08:51, arriving at 13:54 (time 5H:03M, 2 changes - I used Monterosso as an arbitrary destination.... it will be the shortest trip as it's at the north end of the C.T.).
- Monterosso to Roma Termini - the easiest (although not the quickest) trip will be a departure at 09:12, arriving at 14:33 (time 5H:21M, 1 change at La Spezia Centrale.....there's about a 45 minute layover at La Spezia, but as I recall there's a McDonalds in the station so that should keep the kids entertained).
I used arbitrary dates in May to check those solutions. You can save some money especially on trains in Italy with advance purchase train tickets. However these are usually non-refundable and non-changeable once purchased so choose carefully. You can buy advance rail tickets at....
As it's been a few years since you've been in Italy, there are a few potentially expensive caveats to be aware of when using trains and other public transit. If you need more information, post another note here.
You may find it helpful to have a look at both the RS France and RS Italy guidebooks, as there's an enormous amount of information there. You can either check your local library, buy paper copies or download the E-book versions.