Over by the Bastille is Les Caprices de L'Instant at 4 rue Jacques-Cur. They show a small selection in the store, but have a binder with laminated pages listing many, many back vintages of Burgundy and Rhne wines, mainly, but also some older Loires. One of the guys who works there is American and is really great to chat with. I always know if I'm going there, I need to plan to have the time.
Obviously a great wine store overall is Aug, 116 bd Haussmann. Again, many, many great bottles on display, but also ask for a catalogue for what isn't out on the shelves. If you're in town on July 11th, they're doing one of their celebrated tastings, with the theme "Bulle"bubbles of different regions.
Legrand Filles & Fils on rue de la Banque has some older vintages. Caves Taillevent does well in that department, as well. I found something I was told was "impossible to find" there. Also, they sometimes get things from the Taillevent list.
All of these places have impeccable storage, btw. Though one time last winter, a friend and I found the temperature inside Legrand too high. (Some of the stock is with the store, the rest down in a cellar.)
For natural wines, check out Les Papilles on the rue Daguerre in the 14th (not to be confused with the excellent restaurant/wine bar Les Papilles on the rue Gay-Lussac in the 5th, which is also a destination to hit; it's delicious and the wine selection is great).
Bacchus & Ariane is another favorite wine store of mine, rue Lobineau in the St-Germain covered market in the 6th. And there's Caves du Panthon in the 5th. These two don't have older vintages, but the current selection is full of things you'd like to drink.
Other places to eat might, for instance, include Chez Michel in the 10th (rue de Belzunce) or Willi's Wine Bar in the 1sttotal classics, and for good reason. They're both "old school," so I wouldn't use the descriptor "cool," which I will write about next.
Check out tasty food and great wines at Chapeau Melon in the 19th, with a young vibe. Or Le Verre Vol, of course. Or Paul Bert. Or restaurant row over on the rue de Cotte near the March d'Aligre (a great little neighborhood to check out): several great places there (Le Cotte Rti, La Gazzetta, etc.). The old-school working-class Baron Rouge wine bar is amusing, and if the wines are seriously hit-or-miss, they're only like 2.50 a glass and the crowd is joyous and eclectic: hipsters and old lushes and locals.
Also, if you're not doing picnics, you're not doing it right. Get some good cheese and charcut' and a couple of bottles and head to the Buttes-Chaumont park, or the Bois de Vincennes, or the banks of the Seine or the tip of the Ile de la Cit.