Some of my favourite restaurants in Paris.
-Frenchie : 5-6 rue du Nil. Open only in the evening, and closed sat and sundays. There is only one menu, which changes with the seasons. You get to choose between two starters, two main courses, and two deserts. You can add some extras like foie gras (and you should ! it's excellent). Follow the sommeli?res's advices, they know their stuff. Expect a bill of something like 100/120 euros if you get a different glass of wine with each dish. Good luck with making a reservation though, the place is not big so sometimes it can take up to two month to get a table. They speak english, call them and see if you can get in, it's worth it (call between 4 and 7pm (utc+1) from monday to friday.
Note : they have 3 different places in the same street, make no mistake, each is very different ! "Frenchie" (this is where you should go), "Frenchie to go", which is a deli, and "Frenchie-wine-bar" (don't go there, it's overcrowded, and their staff (different from the staff of the Frenchie "Restaurant") can be quite grumpy)
-Verjus : 52 Rue de Richelieu (right next to the Jardins du Palais Royal). Different setting/atmoshpere, but kind of following the same principle : open only in the evening, there is a set menu (7 course), changes with the season, they have an option "accord mets&vins", which means that with each course, they will bring you a glass of wine they think fits the best. About in the same price range. The waitresses all speak english perfectly. Calling 1 or 2 weeks ahead of time should be ok.
You didn't say anything neither about your budget, nor about your "level of wine-knowledge" ; but since you talked about "exceptional wines", if you want to take it up a notch, you should try "Passage 53". It's a two star Michelin (and honestly, it's better than some 3*, I think the main reason why they don't have more is that the place is so small : only 20 seats), you don't get to choose anything (aside from the wine), but who cares, everything is amazing. It's french food, cooked to the perfection by a Japanese chef (Sato Shinichi). Go there for lunch (think 3 hour lunch) since the other two restaurants I talked about are evening-only. Depending on what you take for wines and how much you drink, the final bill can range from around a 100 to thousands of euros.
I kind of hesitated about talking about the following one -not because it's not good, they serve some of the best beef you can find- but mainly because the food is not that original, and to me, if you are going on vacation in France, you might as well try some stuff you can't find at home.
But if you happened to find yourself craving for some delicious beef anyways, try : Le Beef Club (58 Rue Jean-Jacques Rousseau). The wine selection is very large, and ranges from 30-somehting to +1500e per bottles, but I am not really found of their sommeliers, so it's better to go there if you know precisely what you want for wine. If you like "steak-tartare", you have to try theirs (it is "au couteau", with a hint of islay malt), otherwise the "filet de boeuf" is just excellent.
You can get a table easyly if you plan on going there at the begining of the week, or need to book a week ahead (or more) for a friday/saturday night.
At last, not a restaurant, but a place where you should go if you want to do some wine-tasting, or even just to take a look at their amazing wines : Les Caves Legrand (1 rue de la banque)
I hope this helps !
PS : Don't buy wine in Paris (aside from what you'll be drinking at restaurants) if you go to Burgundy. Get your bottles there, it will be much cheaper, and you can go wine-tasting in a lot cellars.
