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Americans visiting Paris are a study in paradox. They love the city's surprises-but only the fully expected, sanctioned surprises, the ones that neatly fit preconceived notions like puzzle pieces.

A penniless musician squeezes an accordion in the crush of the Chatelet Metropolitain station, gunning for tourists' francs while ignoring their cameras. A dyspeptic St. Germain waiter terrorizes four Florida high schoolers, serving them ridiculous cocktails while pretending he can't speak English. Atop Notre Dame, U.S. kids train their lenses on a goat-headed gargoyle, shrouded in scaffolding, that they recognize from the cover of R.E.M.'s first record.

Delight in surprises does not extend to the cavernous Gare du Nord, where three metallic tones boom just before noon on a chilly spring day: "Madames et messieurs," an unruffled voice coos, "due to the late arrival of Eurostar No. 9027, boarding will be delayed for a few minutes. Thank you for your cooperation."

The crowd lets out a sigh of disappointment, and children continue to run through a maze of tourists, snack machines and luggage. Below the platform, past a glass wall, are a pair of handsome navy-and-gold Eurostar trains, sleek with bullet noses like their French cousins, the Train Grande Vitesse.

Eurostar, humming through France's countryside at 180 mph, does one trick that the T.G.V. can't. Sprinting from Paris up to Calais, it dives under the English Channel and pops up on the other side in Dover, England. Three hours after the pistol shot, it crosses the finish line at central London's Waterloo Station.

Since November-a year behind schedule-Eurostar trains have surfed more than a dozen times daily through Eurotunnel's celebrated Chunnel. The voyage's novelty remains strong, and Americans are especially enamored, as they pay only $67 to surf one-way on a tourist-class ticket-half the price of a fare bought in the U.K., and far easier than the traditional train-ferry-train shuffle between London and Paris.

But Eurotunnel has plenty of kinks to work out. British-French-Belgian rail service Eurostar is booked to capacity and is thought to be operating in the black, giving pause to rivals like P&O European Ferries. But start-up delays and operational costs have plagued Eurotunnel, the British-French consortium that leases its rails to Eurostar and owns and operates car transport train Le Shuttle.

Eurotunnel spent more than double its $7.5 billion projection to build the tunnel and bled $600 million in red ink last year, with revenues of only $50 million. And the U.K. tabloids had great fun with an April train breakdown that snarled Chunnel traffic for 4 hours.

With so much recent media hand-wringing, many passengers may have trouble remembering the miracle of civil engineering that first connected the British Isles with Continental Europe several years ago. And that as miners carved the space from both ends, Anglos and Gauls set aside their cheerful mutual hatred for an historic handshake seen worldwide.

Americans, jaded about most accomplishments, do take notice-barely. "" shrieks a young woman in a Harvard sweatshirt. "Am I going to have to sit backwards?"

Despite the cool apology over the loudspeaker, the Eurostar train is precisely on schedule, poised for takeoff at 12:12 p.m. To no one's astonishment, a swarm of American high school students is the last group to board the train, infiltrating the nearly empty Car 2 with chaotic carelessness just moments before departure. Decked out in Banana Republic T-shirts and Michigan State baseball caps, they're as inappropriate to the European experience as a beard on a transvestite.

"Erin, these are so nice! So we sit back there? That's cool!"

"What? I don't know-I think it's just a sit where you can kind of thing."

"Hey, do we get a meal on this?"

No, you don't. But Marie, the train manager, will roll through with a snack trolley before the train hits Calais and the distant coast of France. And she takes French, Belgian or English money. (Hint: if you're American, stay off the francs, worth a paltry 4.9 to the tattered dollar. Americans tempted by Smarties, M&M's and Kit Kat candies in a Selecta machine at Gare du Nord paid a ludicrous $2 for it; a 17-ounce bottle of Coke to wash the stuff down went begging at $3.30.)

Then again, these kids may not notice Calais, submerged as they are in chatter, Rolling Stone and hissing headphones. After reaching saturation on their wide-eyed wonder with Europe, they're exhausted-they might as well be riding the school bus back in Scarsdale.

The train is humming now, gliding through the west side of Paris, with its giant drab housing developments and frenetic graffiti grooving along the walls.

Even the mundane is a sight for Europeans' sore eyes. "I've got a daughter who married a Frenchman in Paris, and I visit four times a year," says a British passenger, Caroline Lumley-Frank, a bursar at a London girls' school. "But I used to have to fly British Airways or Danair out of Stanstead. Sometimes I took the ferry and the train, which I caught at Victoria Station." She winces at the memory of the commutes-5 hours, door to door.

A young French student in the next car, Bettina Blanc, gushes over the innovation: "It's an achievement between France and Great Britain. It's the best way to get from one country to another." Ms. Blanc, studying lingustics and English literature in Brighton, England, is making her second run beneath the Channel. Though she's afraid of flying, she's never taken the ferry; now, as her father works with France's regional transit system, SNCF, her allegiance is with the quicker, more comfortable train.

The scene dissolves into fields and villages, square houses with slanted orange roofs, and then the train blasts through maize fields stretching beneath a half-glorious, half-black sky.

Americans pushing their way to the snack bar run the gantlet of two smoking cars, buzzing with French and Italian travelers who squint through the haze at card games and magazines. Then in the torchiere-lit snack car, more arithmetic-and more jaw-dropping calculations.

Here, the dollar's sad exchange rates are laid bare for American travelers. An 11-ounce bottle of Carlsberg beer runs œ1.60 or 14 French francs-$2.59 or $2.90, depending on how the American plays the cards. Kraft Jacobs Suchard's chocolate Milka bar costs an American $1.21 in British money, $1.45 in French; an Orangina soda, $1.78 or $2.10.

The windows are pitch black, and all that's visible for the next 20 minutes is a procession of dim green lights flying by every four seconds.

Then, just as suddenly, the train is bathed in afternoon sunlight. In Car 2, an American shouts, "Welcome to England!" And a funny thing happens-the entire car is washed in warm applause. The Americans are loudest, natch: Following economically genocidal prices in Paris, they nearly weep with relief at the prospect of London's merely unreasonable costs.

Southern England's aberrantly sunny spring afternoon shines on brown mansions and windmills, green fields and a soccer match at Dulwich College. And finally, it's not just the U.S. kids chatting together-it's the British elders and their American cousins.

Ms. Lumley-Frank, discussing geography with a suburban New York schoolteacher and an older couple from Florida, watches train stations whizzing past into London: Somerfield, Hillenborough, Sevenoaks, Dunton Green, Petts Wood, Bickley, Bromley South, Shortlands, Brixton.

Though she confesses to being bombarded by Eurostar ads (from Young & Rubicam, London) everywhere she turns-on classical and jazz radio, on TV, on outdoor boards, even cruising the Peripherique highway encircling Paris-most of her exposure has been through media attention.

But the media, as everyone knows, has two edges. "I've heard the complaints-it's just the big hype that comes along with anything new. But if the train ever did close," she says with grave conviction, "it would be a tragedy. A tragedy."

But then she laughs. "When I first heard about the Channel Tunnel, I said nothing would take me under the ocean. After I finally decided to go on Eurostar, two school friends took the trip first!"

A 30-second interview with a customs agent is just minutes away, and then the Eurostar travelers can literally walk out of the station and into the center of town. This is the sort of pleasant surprise Americans like about travel in Europe.

Eurostar No. 9027 eases into Waterloo Station, ending Ms. Lumley-Frank's fourth Eurostar journey-a full 15 minutes ahead of schedule.

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