Champagne, Burgundy, Bordeaux, Rhone, the Loire Valley; France is well known as the home of wine.
There are few places in the world where you'll find wine this good at such a reasonable price; perfect for your gap year budget. Beer (lager) is also really popular, especially in northern France, where the 'Biere de Gardes' can be found.
The legal age for buying alcohol is 18 in France. Although this isn't always strictly enforced, take some ID with you when you travel to avoid disappointment.
You can buy wine and liquors from supermarkets, or specialised stores. Generally you'll only find French wines available - 'foreign' wines are a speciality.
Buying a few drinks in a shop and drinking in a nearby park is often a much more pleasurable and cheaper way of drinking in Paris, as doing the same in a cafe or restaurant will always be significantly more expensive. Don't feel self-conscious, you're backpacking! Drinking outside is expected.
There are a few drinks which seem to be more or less unique to France, and nearby francophone countries.