Arc de Triomphe audio guide,
five stops, free.

Stand at the top of the Champs-Élysées and look west, and the arch closes the end of the avenue exactly as it was meant to. That was the whole reason for putting it here. Napoleon's architects proposed the west end of this avenue so that the arch could be seen from the Tuileries palace, the imperial residence down at the far end, and the Emperor agreed.

He ordered it the day after Austerlitz, in December 1805, and signed the decree in February 1806: an arch in honour of the Grande Armée. The foundation stone went in on the fifteenth of August 1806, his birthday, eight metres down between the two southern pillars. After that, almost nothing about this building went to plan.

In 1810 Napoleon married Marie-Louise of Austria and was due to bring her into Paris through this spot, when the pillars were barely out of the ground. So the architect, Jean-François Chalgrin, had a full-size arch put up in painted canvas on timber frames, with five hundred workers hired to finish it in time. The carpenters struck over their pay; six were arrested, and the rest saw their daily wage go from four francs to twenty-four. Chalgrin died in January 1811 with the real pillars about a dozen metres high. When Napoleon fell, work stopped, and in 1814 one architect proposed simply knocking the stumps down.

It was a king, Louis-Philippe, who finished it, rededicated to the armies of the Revolution and the Empire, and it was inaugurated on the twenty-ninth of July 1836, thirty years after that first stone. Eleven people came. The big celebration had been cancelled for fear that someone would try to kill the king.

What you are looking at is 49.54 metres high and 44.82 wide, and that single great opening is a deliberate quotation of the Arch of Titus in Rome. Now drop your eyes to the two groups at the foot of the pillars. On the left, Jean-Pierre Cortot's Triumph of 1810, Napoleon in a toga being crowned by Victory. On the right, François Rude's Departure of the Volunteers, all wings and open mouths. The sculptor David d'Angers said Cortot's work was made of ice, flawless in its proportions and without a soul, and from here you can see exactly what he meant.

Right at the top, along the attic, runs a row of thirty shields, each carved with a victory. And the arch never got the crown it was built to carry. A plaster chariot by Alexandre Falguière stood up there from 1882 to 1886, weathered badly and was taken down, and after that the idea was quietly given up. The flat skyline you see is the compromise.

Walk in under the great arch and look down before you look up. In the middle of the floor, inside a ring of black posts linked by chains, is a flat slab of granite from Vire with one line cut into it: Ici repose un soldat français mort pour la Patrie, 1914–1918. Here rests a French soldier who died for his country.

The First World War killed nearly one million four hundred thousand French soldiers. The idea of burying one unknown man for all of them was first put forward in 1916, while the fighting was still going on, and the first plan was the Panthéon. It was set aside, partly because the Panthéon had begun as a church, and partly because it is a temple for great men, when the entire point of this soldier is that he is nobody in particular. On the eighth of November 1920 the Chamber of Deputies voted, unanimously, for this arch instead.

Nine bodies were exhumed from the sectors where the fighting had been worst. One was set aside because nobody could be certain he was French. The other eight were laid out in the citadel at Verdun, and André Maginot, a wounded veteran himself, handed a bouquet to a young soldier named Auguste Thin and asked him to place it on one coffin. Thin chose the sixth. He explained later that he belonged to the Sixth Corps, and that the digits of his regiment, the 132nd, added up to six as well. The seven he did not choose are buried together near Verdun.

The coffin was brought under this vault on the eleventh of November 1920, but the grave was not ready, so the dead man was kept in vigil inside the arch, day and night, until the burial on the twenty-eighth of January 1921. The minister of war, Louis Barthou, who had lost his only son, Max, to the war in December 1914, stood over him and cried out, in tears, Long live France.

The flame came two years later. Its burner is a round shield with the mouth of a cannon at the centre and twenty-five swords radiating out in a star, made by the ironworker Edgar Brandt to a design by the architect Henri Favier. Maginot lit it on the eleventh of November 1923, and it has never gone out; veterans' associations rekindle it every evening. After her husband was killed in 1963, Jacqueline Kennedy remembered it from their visit in 1961 and asked for an eternal flame at his grave at Arlington.

Since the burial, parades on this square go round the arch, never through it. The German parade of 1940 kept to that custom, and so did de Gaulle in 1944. Before any of that, in August 1919, a pilot called Charles Godefroy flew a biplane clean through this opening, after circling the arch twice.

Now find the smaller side arches, and the columns of names on their inner walls. Those are 660 officers of the Revolution and the Empire, and a line under a name means the man died in battle. When the lists were unveiled in 1836 there was an uproar about who had been left out. Victor Hugo's father, a general, was not on them, and Hugo lamented it in a poem about this arch in 1837, which ends on the words, Phidias absent and my father forgotten.

You are on the roof, close to fifty metres up, and for the first time the name of the square makes sense. Look down at the circle around the arch. Twelve avenues run into it like the points of a star, which is why this was the Place de l'Étoile, the square of the star, until it was renamed after Charles de Gaulle in 1970.

It was not always twelve. The seventeenth-century plans had eight. The star below you is the work of the architect Jacques Ignace Hittorff for Baron Haussmann, under the Second Empire, and Hittorff did something quietly clever with it: between the avenues he lined the circle with four-storey mansions all built to the same design, so that the square closes in on itself whichever way you turn. Walk round the parapet and count them. The old toll pavilions that had stood at this gate into Paris were pulled down in 1860.

Now face east, straight down the Champs-Élysées. That line is older than the arch by well over a century. In 1667 André Le Nôtre laid out a vista from the Tuileries to the hill you are standing on, and in 1709 the lower part of it was named the Champs-Élysées, after the Elysian Fields of Greek and Roman myth. The Place de la Concorde is 2.2 kilometres away down there, and beyond it the Tuileries and the Louvre sit on the same line. Turn round and the axis keeps going the other way, out to the towers of La Défense. This arch was put here to close that view, and from up here you can see how exactly it does.

The hill itself used to be higher. In the eighteenth century the engineer Perronet cut four or five metres off the top of it. A few years before that, in 1758, an engineer called Ribart de Chamoust proposed crowning it with a sixty-metre elephant, a fountain with concert halls, ballrooms and apartments inside. Louis the Fifteenth turned it down, which is a loss for eccentric Paris and a gain for everyone else.

The Eiffel Tower is one avenue away from you. Further round you can pick out the golden dome of Les Invalides, the colonnaded dome of the Panthéon, the towers of Notre-Dame in the distance, and to the north-east the Sacré-Cœur on the hill of Montmartre.

One last picture, and the least peaceful. In 1871, during the Commune, the Fédérés hauled a battery of cannons up onto this roof to fire back at the army of Versailles. The roof you are standing on was built for a victory arch, and for a while it was a gun platform.