Four days in Toulouse: pink brick everywhere, and Airbus at the end of the tram line

Start where the city puts its own name. The Capitole is the city hall and the opera house behind one long brick and stone front, and the square in front of it is the meeting point for everything: markets, protests, and the rugby team on an open top bus. Several of the state rooms are open to the public free of charge when they are not in use, and the Salle des Illustres is the one to find, a nineteenth century hall of murals in which Toulouse tells itself its own history at considerable length.

Five minutes west is the building that will surprise you. The Jacobins was the mother church of the Dominicans, who were founded here in 1216, and it is a Gothic church built entirely of brick with two naves side by side. At the east end a single column fans out into the whole of the vault, a shape everybody calls the palm tree and nobody photographs successfully. Thomas Aquinas is buried under the altar.

Then walk down to the water for the last hour of light. The Pont-Neuf is neither new nor level, it took the best part of a century to build, and the view from the middle of it is the one that explains the nickname.

Saint-Sernin is the reason medieval Europe knew where Toulouse was. Built from the late eleventh century over the grave of the city's first bishop, who was martyred by being tied to a bull, it was a major halt on the pilgrim road to Santiago and it was built to hold crowds: a nave with double aisles either side, an ambulatory running right round behind the altar so that pilgrims could file past the relics without interrupting mass, and an octagonal brick bell tower of stacked arcades outside. It is usually called the largest Romanesque church still standing in Europe.

Two hundred metres away, in a building of 1523 that was once a hostel for those same pilgrims, the Musée Saint-Raymond holds what Roman Tolosa left behind. The star room is a line of portrait busts from a villa at Chiragan down the Garonne, emperors and philosophers by the dozen, and it is the biggest collection of Roman busts in the country. Ninety minutes is plenty.

After lunch at the covered market, cross to the Musée des Augustins, a fine arts collection housed in an Augustinian monastery with its cloisters intact. The medieval sculpture is the strength, much of it rescued from churches the Revolution pulled down, and the row of gargoyles set out along the cloister walk at eye level is worth the ticket on its own.

Toulouse has built aircraft since the mail pilots of the 1920s, and the assembly halls out at Blagnac are open to visitors, which is rare and worth arranging. The tour of the A350 line takes about ninety minutes, runs through the Lagardère hall, which is among the largest buildings in the world by volume, and has to be booked online at least two days ahead with a passport or ID card in the name you booked under. There is a fair amount of walking and no photography in the plant.

The same ticket takes in Aeroscopia next door, which is where you get close to the aircraft themselves: two Concordes, a Super Guppy, an A300 and an A380, with rows of fighters underneath them and more than twenty airframes in all. Concorde first flew from this airfield in 1969. Allow two hours and expect to lose a child in the cockpit queue.

Come back on the tram and walk the last stretch along the Canal du Midi, which starts at the Garonne here and runs to the Mediterranean. Pierre-Paul Riquet dug it in the 1660s at his own expense and died months before it opened; the plane trees along it are the ones on every postcard, and the towpath from the station into the centre is flat, shaded and about twenty minutes.

The last morning is for the two buildings that are easiest to miss. The Hôtel d'Assézat was put up in the 1550s by a merchant who had made a fortune from pastel, the blue dye extracted from woad that made this city rich until indigo arrived from India and ruined the trade. The courtyard is the finest piece of Renaissance architecture in Toulouse and free to walk into; upstairs, the Bemberg collection runs from Cranach to Bonnard in rooms that feel like a private house.

Then the cathedral, ten minutes east, which is the strangest building in the city. Saint-Étienne was started, abandoned, restarted on a different axis and never straightened out, so the nave and the choir meet at an angle and nothing lines up with anything. It should be a disaster. It is oddly moving instead, and the archbishop still works in it.

Matabiau station is a quarter of an hour away on foot from there, or one stop on the metro if you have a case.