Le p'tit Zinc
According to some people, this could be the oldest restaurant in the Old Town.
And it has for sure an "old bistrot" atsmophere and is perfectly located.
The menu has local fish and local cheese dishes (they are buying the cheese in one of the best cheese shop in Town). So you will find some French classic meals and some local specialities.
For more information please check on their website http://www.ptitzinc.fr/