Paris has a great diversity of tea houses, yet not all tea houses are equal. Here are my favorite tea houses.
The absolute best place to buy tea and tea gear is La Maison des Trois Thés. Don't look for a website, they don't have any. They only sell manually processed, non-flavored teas. They are specialized in Pu-Erh teas, but their collection contains more than a thousand different teas, so whatever you are looking for, you will most surely find it.
One other shop that I like a lot is Le Conservatoire des Hémisphères. A selection of very nice teas and the shop looks great. I only buy non-perfumed teas these days and with Le Conservatoire des Hémisphères it is very simple to buy great teas: just pick any.
A great classic in Paris is "Marriage Frères". They have multiple places in Paris and a very large selection of tea. They do various kinds of teas: non-flavored, very expensive teas, but also flavored, cheap ones. If you are looking for quality teas, be careful what you are buying.
Finally, if you are looking for Japanese teas specifically, Jugetsudo is nice: they have only a few teas, but they are good.