We know this. At around 120,000 feet, on the fringes of space, the air is so thin that a falling human body would travel fast enough to exceed the speed of sound. A skydiver, properly equipped with pressurised suit and a supply of oxygen to protect against the hostile elements, could feasibly jump from that height and, about 30 seconds later, punch through the sound barrier – becoming the first person ever to go "supersonic" without the aid of an aircraft or space shuttle.

Here our knowledge ends. Experts admit cluelessness. Our skydiver could render a mighty "krakoom!" across the high skies or history could be made in utter silence. Immense forces could knock the intrepid skydiver out cold, could peel the skin back from his body or simply cause a little wobble in the midriff, like a playful hug. Nobody is quite sure – but one of two men will soon find out.

They are Felix Baumgartner and Michel Fournier, rival daredevils who have long been formulating plans to travel up to 120,000 feet, far higher than any skydiver has yet been, from there to plunge back to Earth. Their plans share similar elements – helium balloons attached to mansize cradles, space-faring equipment, lots of complicated parachutes – but this pair could not be more different.

Baumgartner is an extreme sportsman from Austria, steely, serious and a parachutist who has completed all kinds of dangerous and newsworthy stunts over his 41 years. His effort to skydive from the edge of space – to "space jump" as the feat has come to be known – is backed by energy drink manufacturer Red Bull, who under the project banner Red Bull Stratos have outfitted Baumgartner with expensive kit, a hi-tech Californian base, a team of aeronautic and medical experts and funds fully to publicise the endeavour.

Michel Fournier's mission has not quite the same pizzazz. The French former paratrooper is 66 and not backed by an energy drink. His equipment has been laboriously sourced from various abandoned military projects over two decades and his publicity machine consists of an ill-updated website plus a beleaguered press agent called Francine. Plotting his space jump since the late 1980s, he was long ago banned by his own government from conducting the project in France (too dangerous) and has for the last 10 years been operating from a tiny airstrip in North Battleford, Canada.

Here, Fournier has made several attempts at a space jump, but all have gone wrong in the early stages – the very early stages. He has set a few records – highest skydive by a Frenchman! – but if Fournier has done anything really newsworthy to date, it has been for the type of exploit heralded by a wry broadcaster saying: "And finally…"

Baumgartner has been plotting his space jump for four years, Fournier for 20, and this autumn both projects are coming to a head – 50 years exactly since anyone even came close to leaping from such heights or plummeting at such speeds. That was Colonel Joseph Kittinger, a test pilot, who completed a series of high-altitude jumps from a helium balloon in August 1960, part of an equipment-testing project for the agency that would become Nasa.

Jumping from 102,800 feet, Kittinger fell at 614mph, about nine-tenths the speed of sound; a torn glove meant one of his hands swelled to twice its normal size. On a previous test jump, from 76,000 feet, a parachute cord wrapped around his neck and Kittinger passed out mid-fall; he was saved from death only by the automatic deployment of an emergency chute.

Every year since, says the American, now 82, some privateer has contacted him with plans to beat the record, to jump from higher and travel faster. No one has managed it. The effort has defeated, humiliated, pauperised, even killed challengers since 1960, largely due to the sheer difficulty of getting up high enough to attempt a jump.

It can't be done from an aeroplane (even a spy plane can only ascend to about 80,000 feet), nor from a rocket (any hopeful parachutist opening the hatch to jump out would be torn to pieces). Ballooning directly up is the only realistic option, but an option still fraught with difficulties. A helium balloon launched into the stratosphere needs continually to enlarge because of the changes in atmospheric pressure, and so must be made of a special expandable material that is less than a 1,000th of an inch thin; clingfilm thin. It also needs to be huge, about the size of an office block.

Inflating a building-sized balloon out of something like sandwich wrapping is not easy, as Michel Fournier can well attest. Preparing to launch his first space-jump attempt from North Battleford in 2002, a filling tube on his balloon tore, ending the mission before he'd even got into his capsule. In 2003, he was back on the same strip of tarmac, but the material ripped again, the mission aborted for a second time.

Raised on a farm in the Auvergne, Fournier joined the French army in his teens and rose to become a parachute officer and later a reservist colonel. In 1988 he was chosen by the European Space Agency to be part of a space-jumping effort that was soon nixed by budget cuts; nonetheless a seed had been planted and Fournier – bouncy, rubbery-faced, with an oft-described physical resemblance to Robin Williams – has pursued the project independently ever since. "I haven't led a very conventional life," he says. "I have to live at 1,000mph!"

Or, at least, 700mph – the kind of speed he could expect to reach during a successful space-jump. And so in 2006 Fournier returned to his North Battleford airstrip, newly equipped and ready for a third go. This time he was foiled by unfavourable weather, jet winds that might have carried him anywhere in Canada. In 2008, he was back again, his balloon reinforced with extra layers, Fournier in the capsule below, poised and excited and 20-years ready – when without warning his balloon floated away, the capsule unattached and left behind. A release-switch had fired prematurely and the balloon, worth around £120,000, flew off, landing in ruins miles away.

Nonetheless, for Fournier, "doing crazy shit for as long as possible is the only way to be". He reveals that le grand saut (or "the big jump"), as he calls his endeavour, has just about bankrupted him, that he has sold his car, his furniture, his war medals, even his house. "The main difference between Felix and me is means," he says. "If he has a problem with his balloon or anything else, Red Bull will cover it."

Red Bull will cover it – the company has ploughed billions into the sponsorship of sports as varied as football and Formula One, surfing and sailing. The biggest part of their portfolio, however, has always been extreme sports, and Felix Baumgartner has risen to become one of the company's stars.

He grew up in Salzburg, Austria, idolising Neil Armstrong, Spider-Man and James Dean. Determined and competitive, he always wanted to be the best at things, he says, "even in the sack race at school", and joined the Austrian army, there becoming a tank-driving instructor, a close-combat specialist, and a member of the military's parachute display team.

By the late 90s, out of the army, Baumgartner was making a name for himself in the sport of base-jumping, which required parachuting from a standing start off things such as buildings and bridges. "It came very close to my idea of being able to fly." In 1999 he set a world record by jumping from the Petronas Towers in Kuala Lumpur. Four years later he became the first man to cross the English Channel in freefall, soaring for miles wearing a wing made of carbon fibre.

Luke Atkins is a close friend of Baumgartner, and an experienced parachutist himself. "There are three things everybody asks you as a skydiver," says Atkins. "What's the highest you've jumped from? What's the lowest you've opened your parachute? And have you ever worn one of those wing suits?" In an outrageous base-jumping stunt in Oman in 2007, Baumgartner had popped his chute less than 100 feet from the floor of a cave. "The only thing he hadn't done was jump from the highest."

Enter Red Bull. From 2006 to 2010, the pieces of the Stratos project were put together: a team of ex-Nasa scientists were assembled to do the hard planning; a documentary crew was invited to film preparations; and Luke Atkins was roped in as an extra to hurl his body around at the California HQ when Baumgartner was at home in Austria, riding around on his collection of vintage motorbikes.

Red Bull Stratos made one more intriguing signing: Joe Kittinger. He was persuaded to lend his name to this project after decades of saying no to wannabe space-jumpers because "they were doing it right, safe". Most of those who had contacted him in the past, says Kittinger, "had no idea of the hazards. I didn't want to be associated with people who died in the attempt."

Before hopping from his balloon-attached capsule, Kittinger had described to a ground-control team his surroundings at 102,800 feet. He saw "an absolute void" – "beautiful but hostile". It will be worse at 120,000 feet, where Baumgartner or Fournier will be exposed to the combination of a freezing cold atmosphere and the sun's unfiltered rays. Other risks include hypoxia (a lack of oxygen), decompression sickness, even hallucinations – all before leaving the capsule. Any breakage or failure of equipment at this point would be catastrophic; were the suit to lose its pressurisation, for example, it would trigger a process called vaporisation whereupon the blood, in the vacuum of near-space, boils inside the body. (It was this that made Kittinger's hand enlarge so grotesquely in 1960.)

The plunge itself, lasting around 10 minutes and including a five-minute float once the main parachute is deployed at 3,000 feet, should be relatively easy. All excepting that small matter of becoming the first humans to test-puncture the sound barrier. "That is the real unknown," says Red Bull Stratos's medical director, Jonathan Clarke. "And it's a real big unknown."

One Sunday in May, the same weekend that Baumgartner and Kittinger were due to conduct a round of interviews with the world's media to promote Red Bull Stratos, Michel Fournier was back on his airstrip in North Battleford. A fresh series of preparations had begun for the Frenchman back in January, around the time that Baumgartner had officially confirmed he was to attempt a space-jump in 2010. Fournier ordered a new balloon: his fifth. Probably wary of rousing the same pack of local journalists and science writers who had trooped out to the airfield so many times in the past, Fournier kept his plans quiet. A small crowd, nevertheless, made it to North Battleford to watch, mostly ballooning enthusiasts but also the mayors of two local towns, and Fournier's close friend Gil Bellavance. "I gave him a little salute," recalls Bellavance.

At the far end of the airstrip, Fournier's team were ready to start inflating the balloon, a process that once started cannot easily be stopped. They were told something had gone wrong: the fittings on Fournier's suit were giving him trouble. An hour later, the inflation team got word to start again; this time they got halfway through, the balloon starting to rise promisingly from the tarmac, before a second call to abort went around North Battleford. In his capsule, Fournier's parachute had popped open, three hours and 120,000 feet too early.

"I didn't hear Michel say anything," says Bellavance, "he had his helmet on. But I would imagine the word at that moment would not be printable." On the airstrip, the balloon was deflated and packed away. Fournier's capsule was craned back to its hanger. Around the edges of North Battleford, the enthusiasts dispersed.

"I will do everything in my power to reach the end of my dream," says Fournier, who has tentatively scheduled another attempt, his seventh, for the coming months. But if the end of that dream is Baumgartner getting there first? "I'll congratulate him. But you can bet that I'll do it second."

Should he fail, two decades of botched space-jumps have at least rewarded him with something. A bachelor for most of his life, Fournier met his wife, Kim, in 2003 while she was working as a receptionist at his North Battleford motel. Unable to woo her in English at the time, Fournier simply took her hand and kissed it over the desk. They were married that year.

Baumgartner, meanwhile, has been making final refinements. In one test jump over the California desert he realised that he couldn't twist his head in its helmet to see if his parachute had opened properly, and so mirrors were added to his gloves. His visor, meanwhile, has been fitted with a demister to stop any fogging from his breath. He seems to be on the cusp of history, and has even had time to contemplate a Hollywood film being made of his efforts; Steven Spielberg would be the preferred director.

The exact date of his jump has not been revealed, but it seems likely the attempt will take place very soon, as close as possible to the 50th anniversary of Kittinger's record leap (which passed last month). At 120,000 feet Baumgartner says he plans to take in the view for a moment before jumping. He doesn't yet know what he will say before he leaps, but it ought to be something quotable. ("Stop worrying about death," is one of his lines. "It's like worrying about the sunrise.")

Then he'll bunny-hop from the platform, feet first, in a position long practised because it will ready him best for the strangest skydive of his life. The atmosphere will be so thin and featureless that, at first, he'll feel the sensation of being completely still. In fact, he will plummet faster than anybody has yet travelled outside of a machine. Even if there is a "krakoom!" across the skies it will happen far, far behind the falling man. Baumgartner himself will simply hear a small beep in his ear, confirmation from his equipment that the mission has been a success, and that he has become the world's first supersonic man.