storing luggage while sight-seeing around downtown Paris

Four of the main train stations have "left luggage" facilities where you can store your bags for a fee. They're all security-checked, so make sure you leave some extra time when you pick them up, in case there are lineups. Facilities are available at Gare du Nord, Gare de Lyon, Montparnasse, and Austerlitz. All are easily accessible by metro or RER trains.

Now that it has been upgraded, add Gare de l'Est to the list.