Il pleut dans mon coeur (it's raining in my heart)

Comme il pleut dans la ville (as it is raining in the city)
Because it is rainy in Paris right now. No matter what the weather, as Audrey Hepburn said, "Paris is always a good idea."
So, what is good to do in Paris when it rains?  Spend time in a museum.  Don't just choose one of the big ones, try a smaller museum, like the Cluny, which features medieval art housed in a small castle. Also in the Cluny?  Ruins of a Roman bath.
There is shopping in the Galeries Lafayette and spending some time in the cafeteria on the 6th floor of the main building.  Sit right next to the little ladies who have tea aroud 4 pm, and look out over the rainy rooftops from the windows.
Explore one of the many passages that are covered walkways.  There are shops that feature vintage, well, everything, and some cafes where you can still watch the people pass by.
Speaking of cafes - try one of the beautiful cafes that dot the city.  Want to be chic and have a cognac where the intellectuals spent time?  Try Aux Deux Magots in the 5th arrondissement.

Or, you could just put up your umbrella and take a walk in the rain.  Stroll through the Tuilerie Gardens, or maybe even the Luxembourg.  Listen to the drops on your umbrella, or enjoy just getting wet in the Parisian drizzle.
Whatever you choose remember - Paris is always a good idea.