It can happens, but most of the time, the waiter (or more probably the owner) will propose it to you.
Tell them it was very good (they will ask), but it is a shame that you are stuff and can't finish.
If it's possible, they should get the meaning, and propose it to you.
It happens multiple times with my parents. My parents even got some bones for the dog (the real doggy bag^^).
It happens mostly in independent, family-owned restaurant.
Additionally, i don't think I remember it happens in Paris, or in big cities, it was more frequently in country restaurant.
It never happened in Branded restaurant.
My advice : feel it before asking.
If you have a good feeling with the Waiter, the owner, if they are not overbooked, if you talked with them (in french, in their native language, or in your own language if they seems fluent in it).
if you make them laugh, if you learn about them and if they learn about you/your country.
Basically, if you befriend them, you can go (and yes, it is "allowed" to "befriend" the waiter/owner of a restaurant in France, that's the French spirit).
PS : for obvious reason it is FORBIDDEN in all-you-can-it buffet (and yet, I'm sure you can get it in reasonable amount if done properly).