Some years ago , I sat on a stone-cut bench in a dark chamber in the catacombs of Paris wearing a headlamp and muddied boots, and listened to the strange story of Félix Nadar, the first man to photograph the underground of Paris. In 1861, Nadar invented a battery-operated flash lamp, one of the first artificial lights in the history of photography, and promptly brought his camera into Paris's sewers and catacombs. Over three months, Nadar—41, moustachioed, with unruly red hair—shot in the darkness beneath the streets. He used 18-minute exposures and, as models, wooden mannequins dressed in the garb of city workers. On the surface, the images of dim, claustrophobic passageways created a stir. Parisians had heard of the vast subterranean networks underlying their streets and Nadar brought this dark lattice to light. The pictures opened up Paris's relationship to its subterranean spaces—catacombs and crypts, sewers and canals, reservoirs and utility tunnels—a connection which, over the years, has grown deeper and more peculiar than in any other city.

Now, a century and a half behind Nadar, I am back in Paris with a group of urban explorers. Our aim is to examine the city's connection to its underground in a way no one has before: we will attempt to walk from the southern edge to the northern, using only catacombs, telecom tunnels, sewers and other hidden infrastructure. It is a 14-mile trek, every step illegal. The six of us—five Americans and an Australian—are prepared for a two- or three-day journey, with nights sleeping in the bowels of Paris. We have packed food, sleeping bags, an arsenal of flashlights and headlamps, and gas meters to alert us to any poisonous fumes in the sewers. It will be urban troglodytism, a walkabout in the wilderness under the city.

Just after 9pm on Tuesday, as twilight falls, we stand in a derelict train tunnel to the south of the city. Steve Duncan, the leader of the expedition, crouches by what will be our entrance into the catacombs, a craggy hole in the wall encircled with graffiti. Steve, 33, is a photographer and urban historian from New York. He has explored and photographed the undersides of cities around the world: the sewers of London, the underground rivers of Moscow, the cisterns of Naples. After each expedition, he has returned to New York to lecture on his findings. Like Nadar, he illuminates the hidden anatomy of cities, changing the way urbanites think about their environment. He stands up, flicks the braces on his chest-high waders, switches on his headlamp and grins: "Everyone ready?"

One by one, we slip into the catacombs, unsure when we'll see the surface again. The tunnel we drop into is rough-hewn and low-ceilinged. We duckwalk, backpacks scraping against the rock, the beams of our flashlights dancing on the walls and cold clear water sloshing around our feet. When we pause, there is silence, the sound of cars on the street blotted out: we are inside Paris, yet utterly removed from it.

Parisians say their city, with all of its perforations, is like a wedge of Gruyère cheese and nowhere is so holey as the catacombs. They are a vast, earthy labyrinth, 320km (200 miles) of tunnels, mainly on the Left Bank of the Seine. Some of the tunnels are flooded, half-collapsed, riddled with sinkholes, others are finished with neatly mortared brick, spiral staircases and elegant archways. These were the quarries that supplied the limestone blocks that make up the grand buildings along the Seine, 18 metres (60 feet) above our heads. The oldest had been carved to construct the Roman city of Lutetia, traces of which can still be found in the city's Latin Quarter. Over the centuries, as the city expanded, quarrymen brought more limestone to the surface, and the underground warren spread like the roots of a great tree.

When Nadar first dropped into the catacombs with his camera, the tunnels were largely empty. He might have encountered the occasional mushroom farmer, or perhaps the Inspection des Carrières, the workers who prevented the tunnels from collapsing under the weight of the city—otherwise, in those days, no one. Today, the quarries teem with activity. Walls are covered in riots of graffiti, chambers gilded with carvings and murals. This is the work of cataphiles, a loose tribe of young, bohemian Parisians who spend days and nights in the catacombs. They throw parties, stage performances, make art, explore the limits of the system. Entering the catacombs is illegal and the police employ a special squadron—catacops—to patrol the network. But they deter no one. The tunnels are like a big secret clubhouse.

We've been underground for about two hours when Moe Gates, the team's map-bearer, leads us into a passageway so tight we have to squirm through like worms. We emerge into a large chamber with walls covered in murals. Some of the paint still smells fresh. The floor is littered with half-melted candles and the debris of parties past: beer cans, cigarette butts, bottles of Jack Daniel's. There are tables and chairs cut from the rock, a crescent-shaped bench. Along one wall is a painting which turns out to be a version of Hokusai's "Great Wave off Kanagawa". The chamber is called La Plage, and is a central haunt of cataphiles.

Just as visitors to the surface of Paris follow a sight-seeing itinerary—Sacré Coeur, Notre Dame, the Eiffel Tower—so do visitors to its underside. Wandering through the alcoves connected to La Plage, we visit a room with a Norman castle and rock-hewn gargoyles, a room heaped with silk flowers, a room lined with paintings of film characters. We encounter four separate groups of cataphiles. On a weekend night, La Plage is as crowded as most Parisian bars.

The cataphiles, whether or not they know it, are essential to our expedition. The painstaking map we use to navigate the quarries, acquired years ago by Steve and Moe, was compiled by elders of the tribe. Other cataphiles over the years have brought power drills and jackhammers underground to gouge small passages in the walls, chatières, which will be vital gateways in our trek northward.

We hike for miles, twisting and ducking, climbing and crawling, jack-knifing our bodies in ways most people never do. We go through passageways as tight as sphincters, into chambers as big as ballrooms. The tunnels are marked with Paris's signature blue ceramic signs, the names corresponding to the streets above. The walls are slick with condensation and give off steam. It is like being inside the intricately folded tissues of a brain. It is a place of palimpsests—layers of graffiti tags from the spraycans of young cataphiles, black streaks from the torches of 17th- century quarry diggers, millennia-old fossils of sea creatures embedded in limestone. We peer up manhole shafts so high it is too dark to see the top. We see relics of the wooden braces later quarry inspectors used to shore up the tunnels. At one point, tromping through the darkness, I shine my light upwards to find a giant, black crack in the ceiling. In the 18th century, there were collapses: buildings and horse-drawn carriages and people walking in the street swallowed by the earth. Stonecutters perished in the cave-ins. But the tunnels today are secure and we do not fear entombment. The catacombs are the least treacherous leg of our journey.

After we've been underground for about seven hours, Steve leads us down a passageway with cobbled walls. It is several moments before we realise that the dry, copper-coloured objects on the ground are human bones. In the 1780s, when the cemeteries began to overflow, bodies were exhumed and carted to the south of Paris. Caravans of black-veiled wagons rattled through the streets, pouring bones into pits. The catacombs contain the remains of about 6m people.

"That's three dead Parisians for every living Parisian," says Steve. He and his camera duck into a nook strewn with ribs.

Nadar was captivated by the ossuaries, the silent piles of disarticulated bones, sorted by type. One of his photographs showed an expressionless mannequin dressed in a billowing white smock, apparently dragging a wagon piled with skulls through a dark tunnel.

Crawling over a jumble of dried remains, we peer up one of the chutes into which bones were poured. They are still in place, a frozen cascade 40 foot high: femurs, ribs, tibias, skulls. It is mesmerising. Before Nadar, the ossuaries had been a destination of dignitaries. The future King Charles X hosted fantasy parties among the bones; Napoleon III took his young son on a tour by torchlight. Not long after Nadar's photographs began circulating, the city opened the ossuaries to the public and thousands of Parisians flocked underground to walk the dark, obscure passageways. They continue to flock: today, people line up along Avenue du Colonel Roi-Tanguy, sometimes waiting for hours for a glimpse of the catacombs.

We set up camp in Le Cabinet Minéralogique, a small chamber with a sculpted display for different types of minerals, constructed by 19th-century quarry inspectors. Liz, Steve's girlfriend, makes pasta with tuna, which we eat by the light of our headlamps. Then we sling hammocks from iron rings in the walls and lay out sleeping pads on the rock floor. Somebody asks what time it is. We are in a subterranean cavity that has been perfectly dark and exactly 13.9°C since it was created, a space never touched by sunrise or sunset, nor any of nature's rhythms. "Underground", says Moe, "it is never o'clock."

We awake to find a woman standing in our room. Her name is Misty, a cataphile who has been visiting the catacombs since she was a teenager. She has been walking the quarries alone, carrying an old wrought-iron lantern with a hissing, naked flame, like an apparition from the days of Nadar. We tell her that we are headed north, beyond the catacombs, towards the sewers. She looks us over and says, "Bonne chance."

A round one in the morning, we leave the catacombs through a hole in the wall, barely wider than my shoulders. It is a chatière, cut from the wall by a cataphile to expand the limits of the network. We've been underground for 27 hours now. Everyone is caked in mud, with grit in their hair. Steve points out that we are moving from a quarry tunnel dug in the 12th century, around the time Notre Dame was begun, into a telecom tunnel built in the 20th century. "An 800-year crawl."

The tunnel into which we emerge is about eight foot high, made of smooth concrete, with a rack of heavy, black telephone cables along one side. If the catacombs are the city's cerebellum, this is a vein, a modest conduit linking the more exciting organs. We are closer to the surface now, no longer so isolated from civilisation. Sounds from above filter down manhole shafts: people chattering in the streets, a dog barking. Through a crack in a doorway, I see an orange glow—the lights from an underground parking garage. Moving through these liminal spaces, we are voyeurs, eavesdropping on the city.

To get in and out of the utility tunnel that runs under the Seine, we have to go above ground, but only for a moment. Gathered at the bottom of a manhole shaft, we discuss the choreography of the exit in anxious whispers. Steve, Moe and Liz had opened this same manhole a few days before on a scouting mission and found a cop standing over them. He had let them off, but another run-in with the police could mean the end of the expedition.

"If they put us in jail," Steve says, half-smiling, "we'll dig a tunnel out."

The manhole we pop is near Saint-Sulpice. We come out by a store selling luxury baby clothing. No police. After a quick dash through the empty streets, we open another manhole near Saint-Michel, and disappear back underground.

The tunnel under the Seine is damp, with dismal, submarine acoustics. Even here there is graffiti, evidence of past interlopers. It is fun to imagine a cross-section of the city: the high silhouette of Notre Dame, the bridges, the river and, deep below, a string of six tiny headlamp beams cutting through the darkness. About halfway across, I remember the first time this river ever entered my thoughts, when as a teenager I read Hemingway's descriptions of the fishermen in "A Moveable Feast": old men in the shadows of Pont Neuf, casting lightly with long, jointed cane poles.

We've been in the sewers about two minutes when someone ahead yells, "Rat!" Big and white, it comes skittering down the run-off pipe, splashing in a rivulet of sewage. We leap up, straddling the sides, as it runs under us.

The stink of the sewers is subtler than you'd think, a creeping smell that follows you home. Our main route is the collector tunnel beneath Boulevard de Sébastopol. It is a large, circular tunnel, lined with brick and flanked by two thick water pipes, one carrying potable water, the other non-potable. At the tunnel's dark junctions are Piranesian tangles of ducts and valves. The air is hot and close, the pipe alive with the sounds of Paris metabolising. Down the middle flows a canal of the city's secretions: a stew of shit, rainwater, garbage, dead animals, and anything else undesired on the surface. The walls are spattered with it. We pass around hand sanitiser and head down a catwalk along one side of the canal.

The pipes in Nadar's photographs of the sewers are gleaming and new. Georges-Eugène Haussmann, the city planner under Napoleon III, had recently gutted the city's boulevards and laid 400 miles of brand new sewer pipes. Engineers lavished money and attention on the city's cloaca. They tested and tinkered with the system: an animal carcass ran the length of the city in 18 days, confetti in six hours.

Today, the rigs of pipes are covered in soot, corroded and sinister-looking. It's been 33 hours, and we are all on edge. We have half an eye on the gas meters that Liz and Moe carry, waiting for the alert of dangerous vapours. Mainly, we are worried about rain. Even a short downpour on the surface could cause the collector to flood. Steve, who knows the world's sewers better than almost anyone, traces a little graph with his finger on a wall, showing the exponential rate at which water would rise during a rainstorm. Up to your shins, your knees, your waist, within minutes. There is a rig of pipes along the ceiling from which hang tattered ribbons of toilet paper, a sign of high tides past. It is hard to fight off the image of the six of us clinging to these pipes, keeping our chins above the flow.

"Remember, everything down here is magnified," Steve reminds us as we step over a rack of pipes. "So even a little spray is going to sound like Niagara." It is around 6am, and above us Paris is waking up. Every few moments, someone showers or flushes and a jet of water comes spraying out of a pipe, sending a shock of echoes up and down the tunnel. It is hell on the nerves.

Parisians of 1861 had never seen anything like Nadar's photographs of the sewers. Walter Benjamin called them "the first time that the lens is given the task of making discoveries". One shows a wooden mannequin in waders seated in the dark, in front of a great skein of pipes and ducts and levers. At a time when western Europe was enamoured of big, industrial machines, the image captivated Parisians. Nadar had revealed a dark, threatening wilderness, but also a technological wonderland, an emblem of modernity. Just like the catacombs, the sewers were a world people wanted to see for themselves.

The first public sewer tours, during the 1867 Paris Exposition, brought visitors through the shit-filled canals on a 16-passenger boat, a luxury version of the vessel sewermen used to clean the tunnels. It had carpeted floors, cushioned seats and glowing lanterns—the sewer workers acted as gondoliers, pulling the boat down the canal. Victorian ladies in gowns and hats glided through the city's ejecta. As an edition of Larousse from that time put it, "Everyone knows that no foreigner of distinction wants to leave the city without making this trip." The lure of the sewers has not waned: people today queue up near Pont de l'Alma, along the banks of Seine, waiting their turn to walk through Paris's digestive system.

Our nest is on the banks of an underground section of the Canal Saint-Martin (above). It is a broad, arched tunnel through which the canal flows placidly. The echoes are soothing. Grey morning light filters through the tunnel's far end. On the surface, brasseries would be opening, waiters setting up tables, laying silverware. We string our hammocks to the railing along the canal and sleep, except for Steve, who stays up to keep watch. Only two hours pass before he spots a boat coming down the canal. He quickly wakes everyone and we slip back into the sewers before anyone on the boat can report us.

The last sewers are long, squared-off corridors, wider and less intricate than the Sébastopol collector. A current of sewage, the width of a one-lane road, roars down the middle. We are haggard now—sleep-deprived, but also loopy from the subterranean miasma we've inhaled over the past 38 hours. We pass around a bottle of whisky to steel ourselves. The catwalk is slippery with shit. Steve pulls a length of rope from his bag, "in case someone falls in".

We are beneath Avenue de Clichy now, nearing the northern boundary of the city. Every few hundred feet we pass a tributary tunnel labelled with the sign of the street that runs above it. While Steve takes photographs from the back of the group, Moe walks ahead with a street map, calling out the names of streets as we pass beneath them and how many metres until the end. As we approach our final manhole, the flow of the sewer canal is growing stronger and sewage is lapping over the edges of the catwalk.

We come to the surface under a bright midday sun, outside the city limits, in front of a Turkish restaurant. Six of us climb out of a manhole in the sidewalk. We have been underground for 40 hours. We bring up in our clothes and hair a potpourri of filth, mud, bone marrow and excrement. When we come up, people on the sidewalk halt. A waiter stumbles. Restaurant patrons drop forks and knives. An old woman in a pink sweater leans on her walker, her mouth a perfect O. They peer into the darkness of the open manhole behind us, and I can see them imagining the spaces we've traversed, dark corridors beneath the city. The images in their heads are perhaps born of Nadar's sombre and eerie tunnelscapes from a century and a half before. We collapse on the grass of a nearby park and Steve clicks through his camera: another set of photographs to circulate in the Parisian unconscious.