Family vacation

Your question is too broad to answer. Perhaps if you did more research, and included more specifics such as budget, length of trip. interests ( art, food, history, hiking, etc) , travel style (will you have a car), answers could be more helpful.
Safe travels!

Welcome to the RS forums!
Pat is spot on; the more you can tell us, the better people here can help you. Some of that information should include:
When this trip will be?
For how long?
Whats your definition of "Northern Italy"
What your group wants to do while in Italy?
What sorts of "amenities" are you wanting?
How you plan to get around?
If any of you have traveled in Europe before?
Age span of the 11, and if any have mobility limitations?

Moving 11 people around takes planning, especially if it involves rental vehicles (you would need several) and doing the research on the rules and regs of driving in Italy. Staying "outside" of towns can often require a car to efficiently get around. Non-resident vehicles face access and parking restrictions in the cities and many towns, and practically all infractions (including speeding, driving in bus lanes, entering/exiting ZTL zones, etc.) are registered on camera with 2-level fines - one by the rental company for providing your info to the authorities, and another by those authorities- often issued months after the fact. You'd also be dealing with car seats, and each driver needs to obtain a International Driving Permit.

Obviously, some people DO choose to travel by rental vehicle and do it successfully so I'm certainly not saying "don't" but you have to consider the comfort zone of each appointed driver and their willingness to do the homework. There's a free "Definitive Guide for Driving in Italy" on this website (way down near bottom of the main page) that will be helpful:
https://italybeyondtheobvious.com/about/travel-philosophy/

Staying IN a town or city is often recommended for group of diverse ages and interests, and especially so if they're first-timers abroad. That way you can make use of the efficient Italian trains (no carseats needed) or other local transport to/from airports and walk to many sightseeing attractions, dinner, etc. It also allows a diverse group to more easily split up and do different things at different times. Enjoy wine with dinner? Italian DUI laws are very strict but we don't have to worry about it with our own two feet or local transport at hand.

You may also want multiple apartments versus a single house to have enough bathrooms and 'real' beds for all versus the pullouts that often pass for them in rental properties. Those pullouts can also be located in shared public living areas so the details are important.

Sorry this was lengthy but lots to consider? :O)

perhaps it would work well to combine your two questions, "Northern Italy" and "Southern France" into an overview of what you are after, answering the narrowing down questions above, and then we can help you split it between the two countries?