Museums and galleries: If you happen to be here on the first Sunday of the month, take advantage of the museums, all of which open their doors for free. Many of the art galleries are free all the time anyway.
Visit the markets: Marché des Capucins, Bordeaux's main covered market hall, is an epicurean journey through France, with fresh fruits, vegetables, meats, seafood, breads and pastries - many items you can sample for free.
Street art: Bordeaux's street art scene is second to none, so wander the streets in search of giant murals; head to the Bassin a Flot district or the hipster Darwin quarter which has a large concentration of works.
Festivals: Bordeaux's Fete le Vin is the big one, where you can sample wine until your heart's content - but there are free events happening on all the major squares throughout summer.