Musée de Cluny audio guide,
five stops, free.

Look up before you look at the stones. The vault over your head is more than fourteen metres high, and the Romans built it at the turn of the first and second centuries. This was the frigidarium, the cold room of the largest public baths in Roman Paris, which was then called Lutetia. People came to wash, exercise, have their hair cut and talk, and the cold pool is still here in the room. It is the one part of those baths that keeps its full height, and the museum grew up around it.

Now the four carved blocks. They are older than the room. This is the Pillar of the Boatmen, made between the years 14 and 37, under the emperor Tiberius, and it is the oldest monument in Paris. The boatmen were a guild of shipowners and traders who worked the Seine, the nautae Parisiaci, and their Latin inscription says they set this up publicly, to Jupiter Best and Greatest and to the emperor.

That sounds like a loyal Roman offering, and it is one. But look at who else made it onto the stone. Beside Jupiter, Vulcan and Mars stand gods the Romans did not bring with them. Esus, chopping at a tree with an axe. A bull with three cranes perched on it, labelled Tarvos Trigaranus. And on the top block, a bearded head with the antlers of a stag, and a torc, a Gaulish neck ring, hanging from each antler. The letters above him spell Cernunnos. This pillar is the only place where that god's name survives beyond any dispute.

On another face the boatmen themselves march with shields and spears. Carrying arms was a privilege the Romans granted, and it tells you how powerful this guild was. It is the first society of Paris that we know by name.

The pillar did not stay standing. In the third century its blocks were broken up and used to shore up walls on the Île de la Cité, and they lay there until workmen digging under Notre-Dame found them early in the eighteenth century. Not everything came back: for three of the four tiers, only the top half survives. Whole, it would have stood about five metres twenty high, and nobody knows for certain which way round the blocks were stacked. There are sixty-four possible arrangements.

The stones look pale today because in 2001 restorers cleaned off the black grime of three centuries. The walls around you had their own restoration in 2009, which found that the plaster was once pink, with tiny traces of an intense blue. In those colours, with the cold pool full of water, this was the room.

In the same room as the kings stands a tall white figure, and the first thing to notice is that he is naked. In the Middle Ages the nude was rare, though not unheard of, and a naked man two metres tall, carved in Parisian limestone, is not something Gothic sculptors made often.

He is Adam, and like the kings he comes from Notre-Dame, though from inside the building. He stood on the inner face of the south transept, beside the portal, and he had a partner: an Eve on the other side of the door, now lost. Above them, at the top of the gable, sat Christ of the Last Judgement. The statue was made around 1260, while the architect Pierre de Montreuil was in charge of building the south transept. The museum thinks Adam may be by his own hand, and was at least made under his direction. The clue is in the fig leaves, whose crisp, lively carving matches the foliage on another of his works in this museum, the portal of the Virgin chapel from Saint-Germain-des-Prés.

Look at his raised hand. It is a warning. The priests who came through that door on their way back to the bishop's palace passed right beneath him, and Adam, the first sinner, points them to his fall, and to the Christ above him who redeemed it.

Now look at how he stands. His weight is on one leg, the other is relaxed, the hip swings out, and the left hand comes down in front of the fig leaf. That pose is ancient. It is the pose of the Aphrodite of Cnidus by Praxiteles, the modest Venus of Greek sculpture, and it explains why this Adam has a curve to his body that looks almost feminine. The face has something classical about it too. Only the hair, those tight rolling curls, is pure thirteenth-century Paris. Whether the sculptor had seen an ancient statue, or knew one only from drawings in a sketchbook, nobody can say.

He was not always white. The whole figure was painted, and a little of it survives, most of all on the fig leaf. After the Revolution he was taken down and shown at the Musée des Monuments français. When that museum closed in 1816 he went into a stone store at Saint-Denis with other sculptures whose buildings had gone, and only in 1887 was he sent to Cluny. He has been heavily restored twice since, in 1888 and again at the end of the 1970s. The warning hand has been raised for more than seven hundred and fifty years.

Six tapestries hang around this room, all on the same red ground. In each one a young woman stands on a blue island of flowers, with a lion on one side of her and a unicorn on the other, and rabbits, foxes, lambs, birds and monkeys scattered over the red around them. They were designed in Paris around 1500, and they are the most famous thing this museum owns.

Five of them are the five senses. The museum reads them in the order medieval writers ranked the senses, from the most physical to the most spiritual. Touch: she holds a banner in one hand and just brushes the unicorn's horn with the other. Taste: she takes a sweet from a dish to feed the parrot on her gloved hand, while a monkey eats at her feet. Smell: she weaves a crown of carnations, and behind her a monkey holds a rose to its nose. Hearing: she plays a small organ while her maid works the bellows. Sight: the unicorn has put its front legs in her lap and gazes into the mirror she holds up. Look closely at that mirror. The face reflected in it is not the unicorn's.

Then the sixth, the one nobody has managed to settle. The lady stands in front of a blue tent. Woven across the top are the words mon seul désir, my only desire, with a letter A on one side and a letter I on the other. Her maid holds out an open box, and the lady's hands are at a necklace. Is she taking it out, or putting it back? One reading makes this a sixth sense, the heart, the one closest to the soul. Another reads the whole set as a story of courtly love, in a garden full of plants and animals that hint at it. The letters may be the initials of Antoine Le Viste and his wife Jacqueline.

The Le Viste arms are on every banner: red, with a blue band and three silver crescents. The family had risen fast through the law courts of Paris, and they wanted everyone to see it. The patron was either Jean the Fourth Le Viste, who died in 1500, or a younger relative, Antoine. The figures were drawn by the painter Jean d'Ypres, who also illuminated books for Queen Anne of Brittany. Where they were woven, nobody knows. Brussels, Tournai and Paris itself are all possible.

They very nearly did not make it. They are first recorded in 1814 at the château of Boussac, in the Creuse. In 1841 Prosper Mérimée, the inspector of historic monuments, reported them and worried about their fate, and George Sand wrote of curious, enigmatic tapestries. In 1853 three pieces were described lying rolled up in a corner of the Boussac town hall, with rats and damp eating at the edges. Only in 1882 did the town sell the set to the State, for 25,500 francs. Much of the damaged lower edge was rewoven over the following ten years. One restorer gave up, defeated by what he called an impossible red.

Before you go, look at the leaves. Some are blue. They were woven green, and on the front of the tapestries the yellow in that green has faded away. On the back, which almost no one ever sees, the greens are still green.