This is two Parises in one short walk: the loudest food market in the centre, and the quietest courtyards behind it, where furniture has been made for four hundred years. Do it on a morning — the market is gone by early afternoon, and it's shut on Mondays.
From Ledru-Rollin, walk east to Place d'Aligre. Start inside the covered Marché Beauvau for the butchers, the cheese, the Italian traiteur (deli), then out to the open-air stalls — the cheapest fruit and veg in central Paris, sold at a shout. The grocers expect you to say what you want, so say it. At the rue de Charenton end, the small daily marché aux puces (flea market) is worth a rummage for crockery and the odd good lamp.
Then the switch. Back on rue du Faubourg Saint-Antoine, slip through the carriage doors into the Cour du Bel-Air, and on to the Passage du Chantier — a cobbled lane of cabinetmakers and restorers, the most intact survivor of the quarter's furniture trade. Walk it to the end. Faidherbe–Chaligny is a few minutes further, and takes you and your shopping home.
