Family doing a Europe Trip - need some ideas!!

That sounds like a large Tour, the usual way.
I would recommend you to take the train, as it is certainly more comfortable for your kids,
there are various Family reductions, but they may differ from country to country, you should check the various websites.
In General when buying your Tickets, never pay more than listed here: click here
Tickets may also be purchased electronically (France, Italy, Germany, Switzerland, Austria)

About your Itinerary:

I have the feeling that you're doing a "classical" Europe trip, which will lead you to what was considered "Europe" during the cold war,
which will let you miss many interesting parts.
I think you should skip greece and be exactly aware of what you want to do in Southern France and Italy.
The Questions are: Why exactly southern France ? (and what Part of it), What Part of Italy (Venice or Sicily or something else) ?
If you're heading for Beaches, they will be more or less the same at both places, but I would recommend
you to go to the south-western coast of Italy (less windy), or even better Croatia, where you will find also many quite cheap apartements.

If you can you should stay in a medium-sized Town from where you can reach places around for Daytrips, but will still allow you to have good beach close to the House/Hotel

If you want to stay in a house in a "small pittoresque village" you will need a car (in order to get there without too much probelms - and in order to get around during that week) - and when you are 5 the car will probably be cheaper then trains/busses.
Car shaold be returned in the country rented (best same city) - unless money isn't a problem.

Note that such houses are rented Saturday-Saturday
Look for them at "Gîtes de France" (all on the net)

There are some villages with train/bus access that are picturesque ..

But WHERE in the south of France? Cote d'Azur or the south of France????

Kira