Someone asked for this, so I'll start the ball rolling. Bear in mind that I only drink tea when I have a bad cold...and am no expert! This is a list of things that you will find in an average cafe. Trips to tea salons are a little different, and I will leave that the experts.
"Un the nature" ( uhh tay nah-TOOR) = plain tea, no milk.
"Un the au citron" (uhh tay oh see-TROH) = the same, with a slice of lemon.
"Un the au lait" (uhh tay oh LAY) = plain tea, milk on the side.
Tea is served one of two ways, in my experiece - either the bag is on the side, or loose leaves are in the pot, with a strainer.
A small pitcher of hot water is on the side, and you can ask for a refill =
"un peu plus d'eau chaud" (uhh puh ploos dough show)
Usually, in a cafe, there is a small choice of tea - Earl Grey, Oolong, Green Tea = "The VERR" (tay verr).
A nice thing to try is "The a la Menthe Fraiche" (tay ah lah mont FRESH) = Fresh Mint Leaf Tea. The "Fraiche" part is important. This is really nice when it is served in little Moroccan tea pots, meant to be drunk from hand-painted glasses. The little potholders that usually come with this are "la cerise sur le gateau" - that little something special. La Favorite on rue St Antoine and Le Regis on Ile St Louis serve it this way, just to name two places.
Finally, for the last lesson of the day, a good thing to try when you are caffeine'd out or need a restorative is "Une Tisane" (oon tee ZAHN) = herbal tea. The usual ones I have encountered in cafes are "Tilleul" (tee YUHL) = linden flower tea and "Verveine" (verr VENN) = verbena. There is a large array of herbal teas available in health food stores - where they claim to cure any ailment - and herbal-green tea mixes can be found in any supermarkets. If you take any medications, or have any medical conditions, be careful about using herbal teas, as they can have negative consequences, for which I do not wish to be held responsible...
So - let's hear from some real tea experts!