I love Nice and could happily spend a week wandering round the towns on the train line.
Currently trying to put together a trip to Biarritz and San Sebastián, which has been recommended. Maybe that’s something that would interest you?
Not sure if we are wise as we’ll have a two year old and a seven month old, maybe this is the time to swallow it and do an easy package holiday.
Flew to Biarritiz and stayed at a campground ground, Le vieux port at Messanges, traveled quite a bit with the hired car, took in Lourdes one day, another day headed towards San Sebastián. The only problem with that side of France it can be hit and miss with the weather, so with wee ones that’s not a bad thing..
Our child was 18 months at the time… 20 years ago 
I know she (I think?) won’t remember it, but you obviously do!
We booked Bella Italia campsite at Pescheria at Lake Garda instead. One stop easier. Maybe Biarritz/Sam Sebastián next year.
Also going for two wks to Chamonix in July. Superb place and flights weren’t ridiculous to Geneva as it isn’t a popular summer destination for us folks on this island.
Agree that hire car costs are stupid.