As a French native, I discovered this practice in North America. I never asked for a doggy bag in France, nor have I seen someone do it. So it is likely restaurants don't even have boxes.
You can obviously take out food from fast-food restaurants but for regular restaurants I don't think it is correct behaviour. I usually finish my dishes, I only order what I can eat. I believe that is what most people do. Sharing your dish with your friends/family is also common practice. You can still ask to have a small portion if you eat really little, I did not see this that much but I guess the waiter will do what he can.
You can still try to ask, if you are not in a very classy restaurant or a restaurant you go everyday, the worst you risk is an awkward atmosphere when the waiter says no.
EDIT: There is a recent article from the New York Times on the topic, Lyon (a city in France) and the Rhône-Alpes region introduced the doggie bag (called "gourmet bag") in order to reduce food waste. The article describes how the French have a hard time using it. I think it develops an interesting argument that in France, eating out is not seen as "feeding", but more as enjoying a meal, for the fine food and for the place: "Dining out is thus a rare experience, to be enjoyed in situ, not bundled up in plastic foam containers and reheated in the microwave.".
So if you go to Lyon (and you should go ;)), you should be able to ask for a "gourmet bag" without the waiter being too surprised.