The City of Light is magical all year round, but it's particularly gorgeous in June, when the long days (the sun doesn't set until 10 pm) stretch sightseeing hours and make it ideal to linger in the cafés.
Winter can be dark and chilly, but it's also the best time to find cheap airfares and hotel deals.
April in Paris, despite what the song says, is often rainy.
Summer is the most popular (and expensive) season. Keep in mind that, as in many other European cities, some shops and restaurants close in August for several weeks, though there are still plenty of fun things to do, like free open-air movies and concerts, and the popular Paris Plage, the "beach" on the Right Bank of the Seine.
September is gorgeous, with temperate weather, saner airfares, and cultural events timed for the rentrée (or return), signifying the end of summer vacation. In the third weekend in September, scores of national buildings that are normally closed to the public open for visits during the annual Journées du Patrimoine (Patrimony Days).