Its a bit daunting to take in a city with a baby in the rain, so here is a guide of things I enjoy with a toddler in the wet streets of paris.
Soak up the Museums my favorites include le musée de la chasse et de la nature which is photographed above and looks like an old french eccentric's house or the set to a Wes Anderson film. Le musée d'Orsay the converted train station on the left bank, le musée de l'Orangerie for Monet and the impressionists and the Grande Palais for ever changing exhibitions. Of course the Louvre is amazing as well but with the crowds of tourists and dauntingly palatial wings I find it less baby friendly then the three above.
Cafe Hop: One of my favorite memories in Paris is from my first summer living with Michel when we cafe hoped from Bastille to the fireworks at the Eiffel Tower. I finished work in Bastille around 5 and we spent the whole evening walking to the Eiffel Tower, stopping for coffee, wine or beer in any cafe that drew our eye. We made it, a bit weak in the knees but well hydrated, for the sunset fireworks.
Take Photos: Everything is clean and sleek in the rain and you can get great action shots of men in suits and women in heels making mad dashes.
Wander the Passages: Paris is full of Passages. These covered pedestrian walkways are lined with beautiful little boutique shops. The Passage du Grande Cerf and the Passage du Paradise near the Grand Boulevards are a great place to start.