Taking rental car from Italy to France and back, any restrictions?

There are restrictions if you plan to travel to Eastern European countries, but not to France.
In any case it’s a good idea to mention it when you rent.

We often rent our car in Nice, France (much cheaper than in Italy)and spend most of the trip in Italy. No issues at all.

You will need to contact the office you are renting from. They all have different policies. Some will allow it, some won't. If you rent from someone without informing them you are taking the car to another country and you have an accident they can void your insurances.

Donna

Should be no problem for France if rented in Italy.
If you are renting a premium car (or get upgraded at no charge to you when you get there) ; one of the German brands (BMW, Mercedes) for example the contract rules may be more strict about staying within the country.
If a compact or economy type class car it is not a problem.

The contract you should have or will receive should actually state things like this in it.
If the contract verbiage states it is OK, no need to inform the agency of your precise plans.

I can say for certain some neighboring countries like Slovenia are an issue with an Italian rental.
The rental agencies treat Slovenia as Eastern Europe.
As someone above me mentioned it is all about insurance and since Italy includes a base insurance you have to stick to the rules of the contract. In my Slovenia example above only certain car classes were allowed and I had to pay a surcharge to add Slovenia to my rental contract.

There is a yellow pollution sticker issued in France which will be very unlikely to be on an Italian car. Is required to go into the low-pollution areas of most French larger towns and cities. Very similar to the German Umweltplakette (but that one's green).

Solution for both, don't try to enter the low pollution areas without the sticker, stay in the suburbs and take a tram or bus to your destination from the Park & Ride lots.

Of course you will have already obtained your IDP as it is required by law in Italy - it is in France too, but not in Switzerland or Germany.