The spring season is the most popular with tourists. The fall season has many of the same advantages, but without the tourists. Few people visit the city in winter, so if you come then, you'll encounter mostly natives. In July and especially August, many Parisians go on summer vacation, and the city is very quiet, with mostly only other tourists walking around in the summer heat. Paris is much safer than American cities of comparable size.
Crime rates are low overall, and violent crime is very rare.
Crime in general has also declined sharply in the past two years or so, mainly due to increased police activity. Paris isn't any more dangerous than any other city in itself, but as a tourist, you are more vulnerable to what little danger there is. Put succinctly, the risk is in being a tourist, not in being in Paris. More people died from one bomb in that city than have been killed by all terrorist acts put together in Paris. I don't think so.