It has been many years, but over a 4 year stretch, I visited France about 4x per year on business. While it is very much a function of what you would like to do and see, weather should not be a primary consideration. It will be necessary to bring some warm clothes - particularly for someone coming from PHX or TPA - but it should be possible to enjoy most all of what Paris has to offer. While Metro will get you most everywhere, be sure to bring some comfortable walking shoes.
Paris can get quite hot in the summer, very crowded with tourists, so there are some advantages of avoiding peak travel seasons.