Planning a trip for next summer with our young daughter and have taken her to Europe a couple of times.
I would say it slows you down overall a good deal but otherwise there is not really much you cannot do.
In Paris having a stroller proved a unknown benefit at the Lourve, people with strollers in their party are treated the same as handicapped ; no line and VIP escort right into and onto the elevator to the museum. Just stroll right up to the glass pyramid.
I was in shock in a very good way!!!
We took her to Paris last year, she was 3.5 at the time (added a day at Disneyland Paris as a treat for her) . Maybe too young at 2.5 for that though it is a nice easy train ride from Paris and glad we did it.
My daughter absolutely loved watch the Eiffel Tower sparkle at night ; happens for 5 minutes or so every hour on the hour from dark until Midnight. She still talks about it to this day.
Anyway going back to Paris next summer just for a quick stop and plan is to do the Riviera and Provence after that.
While I understand from personal experience how a car can be a big plus with a 2,5 year old in tow
Depending on where you are staying on the Riviera you may be better off with a car, traffic is bad, parking is tough, expensive and with the train along the coast you can reach most every town via the train and in some cases ferries.
April may be better than summer when we are going.
I think your best option is to take the TGV train from Paris to Nice, many departures and takes less than 6 hours I believe which is faster than you could drive it, that is the high speed train. I think it would be as quick as flying when you add time to get yourself to the airport, security, etc... plus the train gets you to downtown Nice not 20 minutes away that the airport would. From the train station you can also reach the other towns.
I looked into flying, renting a car at either Dijon or Lyon, etc... as well. By the way I heard renting and driving out of Dijon's train station is far easier than Lyon but have no actual experience doing it.
Eze I am curious why that is not good for a toddler?? it is definitely a town I want to check out though probably will not stay overnight in (not many hotels and we may want to be closer to the beach ; not staying long enough in the region to have more than 1 base personally)
I am thinking we will not rent the car until leaving the Riviera but have not figured out where to rent one yet???
Not sure if we are staying in Villa Franche or elsewhere yet, I plan on driving to Moustiers after the Riviera though and need a car for that area.