France is basically without coffeeshops (Starbucks aside), but there are in Paris a number of exquisite spots for grabbing a pot of tea and slice of tarte. Here are my favorites:
Located in the Marais, just a few blocks from metro Saint Paul and down the street from l'As du Falafel, Le Loir dans la Théière (the mouse in the teapot) is a charming cafe serving lunch, extremely popular brunch on weekends, and generously-sized slices of tarte. My personal favorite is the tarte au citron, a Frenchified version of lemon meringue pie which could easily send you into insulin shock.
The atmosphere is almost that of American coffee shop, with plush armchairs and coffee tables interspersed among regular table-and-chairs seating. The formule thé will put you back 10€, but you can economize by getting an additional thé and sharing the tarte between two. A cheery spot to find a little warmth during Paris' cold winter months (hint: in case of frozen fingers and toes, the table to the left of the entrance is adjacent to a radiator).Le Loir dans la Théière
3, rue des Rosiers 75004
01 42 72 90 61, Monday-Friday from 11h30-19h. Saturday and Sunday from 10h.
For a slightly more upscale experience, there's A Priori Thé located along the covered passage Galerie Vivienne near the Palais Royal. Popular cheesecake, crumble and tarte are available in half portions for ~4€, coffee/tea/hot chocolate 3-5€. Try and get a seat "outside" in the passageway in order to best admire the beautiful setting. 
Brunch here is reportedly quite nice as well. Go early to avoid a long wait, and try the scones, served with little pots of assorted jams and cream. A Priori Thé
35-37 Galerie Vivienne 75002
01 42 97 48 75, Monday-Friday 9h-18h, Saturday 9h-18h30, Sunday 12-18h30.
My most recent discovery, the Café at the Musée de la Vie Romantique, is an idyllic spot during Paris' warmer months. From mid April until mid october, this outdoor setting provides a respite from the bustle of right-bank Paris (you won't believe you're just a skip and a hop away from the Moulin Rouge). 
Order inside the iron-and-glass solarium, and than take your tray to one of the tables on the gravel lined terrace. Formule thé at 10€, I highly recommend the tarte Amandine. As if the roses and leaf-dappled sunlight were not perfect enough, there is an elementary school next door and during the week, peels of children's laughter float across the ivy-covered wall. A little slice of heaven with your Tea?Café of the Musée de la Vie Romantique
16 rue Chaptal 75009
01 55 31 95 67, Tuesday-Sunday from 11 h 30-18h.
Additional recommendations:
L'Oisive Thé
10 rue de la Butte aux Cailles 75013
08 99 69 57 67, Tuesday-Thursday 12h-19h and Friday-Sunday 12h-20h.
La Charlotte de L’Isle
24, rue Saint Louis en l’Ile 75004
01 43 54 25 83, Thursday-Sunday from 14h-20h.
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La Fourmi Ailé
8 rue du Fouarre 75005
01 43 29 40 99, Monday-Sunday from noon - midnight.
