This place used to be my regular haunt when I was an exchange student living in the 6th in 1997. I used to have tartines, which was all I could afford, and to be fair they were delicious. The proprietor knew I was broke, so he always poured me free sample wines to introduce me to good French wine. In fact the place is mainly a wine store, but keeps a few tables as a restaurant as a side line. Recently, I returned to Paris, and ordered a non-tartine meal, and had a simply unforgettable experience.
Name: Le Petit Luxembourg
address: 29 Rue Vaugirard 75006 Paris. It's in the 6th, not far from the Jardins Luxembourg, around the corner from my old street, Rue Jean Bart.
Recommended: all of the terrines are great, and the salads have proper french vinaigrette. The cassoulet and rillettes are wonderful - they are salty, but I believe that that is how they should be. For a simple, but exquisite chicken dish, the poulet a la Petit Luxembourg is wonderful - an herbal wine and butter sauce. For dessert there are 2 tartes a day made by the owner's wife - we had au citron and the best chocolat fondant ever.
Do not, do not, order your own wine. Instead, ask for a kir to begin with, order your food, and ask him to bring what he recommends. As he operates a wine cellar he will bring you a matching wine by the carafe. We had a 4 course meal for 2 for 50, including 3 different wines, though I think he knocked a bit off since he remembered me from my student days.
His dog is called Pamplemousse (grapefruit). She is very old, so don't pet her, but ask after her health and you will endear yourselves.
Okay, I have let you all in on a big secret, but you will thank me for it.