I can confidently say that Paris is the world's most walkable city-- not only because most neighborhoods are built for pedestrians (with some caveats-- see Paris Safety Tips) but because the city of light's neighborhoods are dizzyingly varied and fascinating. So bring a good pair of walking shoes, invest in a good Paris city street map, and hit the streets for a zero-Euro treat.
Popular Paris Neighborhoods to Explore:
Off the Beaten Track:
In French, the word "culture" has a broader sense that refers to the universal right for all to be exposed to the arts, sciences, and humanities, and to that end, the government funnels lots of funds into making "la culture" accessible to all. Many Paris museums offer entirely free admission at all times, while others, including the Louvre and the Musée d'Orsay, are free for all every first Sunday of the month.
Paris hosts scores of fun, inspirational and entirely free annual events, from arty affairs like all-night public art installations to artificial beaches implanted on the Seine River each summer. Many of these are concentrated in the spring and the summer, but each season hosts at least one or two of these festive, budget-friendly happenings.
Related: Summer Festivals in Paris
Paris houses many of history's more stunning spiritual relics-- cathedrals and chuches that stand today as breathtaking testimonials to a complex heritage of Christianity that dominated in Paris from the fall of the Roman Empire to the French Revolution. Many of these majestic cathedrals and churches fell into near-ruin in the wake of the Revolution, but revived interest in the 19th century brought about their restoration. Many of these are must-see sites no matter your budget-- but the fact that entry is free doesn't hurt.