Spring can be cool and generally rainy.  May to June is probably the best time to go because the precipitation is not too high, the temperatures are warm, although the number of tourists will continue to increase and is generally high in June.  July is a little different...the temperatures are higher, and there are many more tourists.  August is the worst time to go to Paris because it is hot, and much of the city is closed for the annual summer break in August.  The major attractions are of course open, but many small, quaint shops close.  The winter monthes are cold, wet, and windy.  The city is beautiful during Christmas though.

These are all of course generalizations so be sure to check the weather right before you leave.