In order to find an apartment, you'll want first to learn the lingo.  There's some specialized information here:

Short-term. In furnished apartments in Paris, a 'short-term' rental usually means one ranging from a few days to a few weeks. Usually the rental rate is by night or by week.
Long-term. In furnished apartments in Paris, a 'long-term' rental usually means a lease ranging from a couple of months to a year.
Square meters. Apartments are measured in square meters. Not used to meters? Think 10 square feet per meter.
Agency fee. Most agencies charge fees for placing you in a medium or long-term rental. Ask up front; it can cost you up to a month's rent.
1 pièce. This translates as 'one room,' a.k.a. a studio. The kitchen -- which may be an open area in the main room -- and bathroom will also be there, but they don't get counted.
2 pièces. This translates as 'two rooms,' and it means there is one bedroom and a sitting room. The kitchen and bathroom will also be there, but they don't get counted.
3 pièces. This translates as 'three rooms,' and it usually (but not always) means two bedrooms and a sitting room. (The kitchen and bathroom will also be there, but they don't get counted.)
Rez-de-chaussée. Also known as the RDC, this is the ground floor. Usually it's not ideal for a rental, for it means that people walking by at street level can look in and watch you doing your crossword.
Caution. No, 'Caution' doesn't mean 'be careful' -- although you should be wary. It's a deposit, and a month's rent or more may be held until you leave the premises at the end. No fun, but it's pretty standard.