To be honest, Paris is beautiful in almost every season.
A firm favourite would be autumn (fall) in September and October, or spring (April and May) since the city is warm enough to enjoy but the key landmarks are a little quieter than the peak summer months. Summer (June to August) boasts lovely, hot weather but it can be busy with tourists and the queues for places like La Louvre or the Eiffel Tower can be brutal.
If you don’t mind the cold, then the winter months are also a lovely time to visit.