A practical wet-weather Paris plan using covered passages, museums, churches, cafés, and shorter walks.

The covered passages near Grands Boulevards, the Louvre, and the Galeries let you keep moving without getting soaked. Treat them as the spine of a wet-weather day and hang shorter outdoor hops off them.
A focused Louvre or Musée d’Orsay visit, Sainte-Chapelle, and a long café stop carry a rainy day better than a string of monuments. Book timed entries where you can so you are not queuing in the wet.
Rain makes long crossings miserable. Cluster everything in one or two neighborhoods, use the Métro for the gaps, and keep an umbrella plus one backup indoor option in reserve.