It is not common practice as PhilD and Souphie already mentioned. You can however negociate the 'droit de bouchon' in advance if you want to bring your own special bottle.
It wouldn't make sense for an ordinary wine though.
I did it a while ago at l'Astrance (but we also ordered wine a la carte).
I don't believe it is - I don't recall visiting any restaurant that would appear to do it. Wine is freely available in restaurants, cafes and bars so there is no real need to BYO. Obviously it saves money for the diner, but also reduces revenue for the restauranteur.
My understanding is that BYO grew up in countries were there are limitations on the availability/number of liqueur licenses or where these licenses cost a lot of money and are thus uneconomic for small (low cost) restaurants. I don't think these issues exist in France.