Quebec City looks like a French provincial town because it was one first. Samuel de Champlain founded a settlement on the shore in 1608, and the town grew up on the cliff above it. In 1759 the British beat the French on the Plains of Abraham, the colony changed hands, and the French-speaking population stayed. The walls around the Upper Town are the only city walls still standing in the Americas north of Mexico, and UNESCO listed the old town in 1985.
That is why three days is the right length. The old city is small enough to cross on foot in twenty minutes, yet each of its two levels fills a day: the walled Upper Town with the fortress and the battlefield, and the Lower Town with the oldest streets and the best museum. The third day goes out of town to Montmorency Falls and Île d'Orléans. A fourth day would mostly repeat the cobblestones, unless it goes to a winter event or a train to Montreal. Expect French on every sign and menu.
Day one is the Upper Town, day two the Lower Town, day three the day trip. Start on a Tuesday if you can. The Musée de la civilisation is closed on Mondays for most of the year, the free tours of the National Assembly run on weekdays, and a Tuesday start puts the museum on Wednesday and the island on Thursday. More on the country is in the Canada guide. In winter everything still works and the old town under snow is at its best, but days are short and stairs icy.