A lot of Paris is indoors, so it's not difficult to escape the rain. You can go to museums, take in a movie, explore the city's covered passages, visit underground sites like the sewers (it's a lot better than it sounds) or the Catacombs, spend time in a café, visit some of the city's greenhouses, explore churches and cathedrals, take a course or attend a workshop, or shop in one of the city's wonderful department stores.