Paris generally has a moderate climate. In winter, temperatures can dip below freezing, but they usually stay around 45 F/7 C. Often winter is wet and gray, although the rare snowfall disappears as soon as it hits the ground.
Summer mornings tend to be cool (sometimes requiring a sweater), but afternoons get warm. A few summer days get hot (80-90 F/26-32 C). Every so often, summer brings a canicule (heat wave) so check that your accommodations have air-conditioning; most do, but some smaller ones may not. Dress warmly in winter and take along a sweater or light jacket in summer.
Rainfall is more frequent in the winter months, but it can (and often does) rain in Paris at any time of year, so it's always a good idea to pack an umbrella. The best time to visit is is April-June, or in the cool fall months after the tourist season is over. Most Parisians go on vacation in August, so many shops and restaurants may be closed then, and services may be limited as well.