Engulfed in a crisis that is threatening the euro, Europe is coming face to face with a major piece of unfinished business: A decade after constructing a common currency, it has failed to build a single, integrated economy to match.

The debt crisis rocking Rome, Madrid and Athens has plunged the region into a heated debate over a historic step that could see the advent of the euro zone’s equivalent of U.S. Treasurys — a bond jointly backed by the taxpayers of all 17 nations that share the euro. But even that step toward integration — one many nations in the region are fiercely resisting — speaks to only part of the problem.

Even more fundamental is Europe’s inability to create a single functioning economy stretching from the warm Mediterranean waters of Cyprus in the south to the frosty Baltic coast of Finland in the north, a dream plagued by failures to harmonize welfare systems, labor markets, a dizzying array of tax codes and, most important, the drivers of economic growth.

In short, to ensure the euro’s survival, even prosperous large economies such as France must begin to look more like Germany, which cut social benefits and reinvented its economy as an export-driven dynamo in the 2000s.

For proof of the economic divisions tearing at the fabric of the euro, journey no farther than to Lorraine, a French border province of ocher-colored countryside and hard-hit industrial towns where the old bunkers of the Maginot Line — the French border fortifications overrun by the Nazis in World War II — stand as a reminder of Europe’s stakes in forging a common future.

On the highways and cargo trains crossing the France-Germany border, trade flows moderately favored Germany before the adoption of the euro a decade ago. But as the late-model Mercedes-Benzes and BMWs parked in the driveways of French farmhouses attest, their trading relationship today is beginning to look more like the United States and China, with the French buying far more from the thrifty Germans than they can possibly sell them.

After years of sluggish growth, unemployment in France stands at almost 10 percent, nearly three percentage points higher than in Germany. Yet despite herculean efforts at cultural exchange, high schools in Lorraine are witnessing a drop in students studying German. In this province once known as much for its now-fading steel industry as for savory quiche Lorraine, the number of workers who cross into more prosperous Germany actually plunged 37 percent over the past decade.

In a cafe serving coffee and a choice of German pretzels or French croissants, Loic Brastenhofer, a 27-year-old machinist, explains why. Laid off in 2009 from a job at a German-owned steel plant on the French side of the border, he turned down an offer for a new post in Germany.

And who could blame him? On the road to Germany becoming a hypercompetitive export machine, workers there suffered years of depressed salaries and benefit losses during the 2000s, a pinch workers in less competitive France have yet to feel. French workers enjoy a 35-hour workweek, four hours less than in Germany. At nearly $2,000 a month, the minimum wage in France is one of the highest in Europe. Germany has no state-mandated minimum wage.

Unlike a worker moving from, say, Maryland to Virginia, social security between Germany and France is not yet portable, even though they share a common currency. That means Brastenhofer would leave behind some of the most generous pension benefits in the world if he crossed the border for work. He would also need to labor years longer. Germany’s retirement age is 67; France’s is 62.

“In France, the unions make sure we get raises even in hard times,” he said. “Economically, the Germans may be stronger, but socially, they are not. If there were a choice, I would be ready to go back to the [French] franc.”

Fidgeting next to his brother, Nils Brastenhofer, 25, had to jump in. Echoing the kind of dinner-table debates going on across Europe as the region struggles with the hard choices to bolster the euro, he warned his brother in French to “stop being such a jerk.”

“What are you talking about, it would be the end of the world without the euro,” said the younger Brastenhofer, who works in a German-owned factory here making Smart Cars. Without Europe’s help, he said, “Greece would be bankrupt already and living in total poverty. China would be buying up half the continent by now. We are each too small to find a place in globalization on our own, but together, Europe is strong.”

An economic project at risk

Now at a crossroads, European leaders must pull closer together, economists say, or risk the euro project falling apart. For all 17 nations that share the euro, it will mean major sacrifices.

In capitals across the euro zone, officials are fiercely debating a fiscal union that could reassure markets unnerved by the debt crisis that, for example, the might of German taxpayers would stand behind the debts of their neighbors.

But the euro crisis is not just about debt. France and Germany, for instance, shoulder almost the same level of debt as a portion of their economies. Yet last month, a bout of investor panic hit Paris, but not Berlin, amid fears of a French debt downgrade. Analysts say it comes down to fundamental doubts about the economic differences among the countries of the euro zone.

France and Germany adopted the euro and virtually erased their border in the 1990s, a time when European elites saw the two nations as the core of ambitions to unite Europe into the world’s single largest economy. The hope then was that the economies in both nations would converge and grow with the rest of the euro zone, as the single currency and open borders became a rising tide lifting all boats.

But things have not quite gone as planned.

“If you look at how many French companies sell to Germany, and how many German companies sell to France, you can see that each side of the border is like a different world,” said Jean Pisani-Ferry, a French economist and director of Brussels-based think tank Bruegel.

‘Huge cultural issues’

In a hidden industrial quarter of Metz, Lorraine’s largest city, Claude Caillet, 63, walked among the cobwebs of his old factory floor.

Dating back to 1950, his company, Sitelec Moselec, a French engineering and auto industry manufacturer, employed nearly 310 workers in its 1990s heyday. But after years of declines, Caillet was forced to file for bankruptcy in October 2009.

The story of Sitelec, in many ways, tells the story of French manufacturing and why the sluggish economy in France — a nation dominated by massive corporations heavily reliant on state contracts — has failed to keep pace with Germany’s fast growth in recent years. Caillet’s company was one that is increasingly rare in France — a small manufacturer totally reliant on private sales.

His firm designed and manufactured the machines used to make cars inside the plants of large French automakers. But in the early 2000s, those plants began turning to cheaper manufacturers in China.

Caillet struggled, he said, to reinvent his business. At one point, he sought to emulate the model in Germany — where small and medium-size companies have reached meetings of the mind with labor unions and dominate the economy by carving out highly specialized niches. But as Caillet tried to remold his firm, he said, tough French labor contracts left him no room to furlough workers, and he found his staff reluctant to retrain for different tasks.

“We have huge cultural issues to deal with in France,” Caillet said. “There is no will to make the kind of sacrifices the Germans did to become more competitive. To get there, France will take a while, and I’m not sure we have that much time.”

The euro’s role as glue

Crossing the border farther south, French pastures give way to the foothills of the Black Forest, and the tiny apartment where Andres Boehme, 50, lives with his wife and two sons in the German city of Freiburg. His sprawling apartment complex, he said, was once a base for Nazi soldiers. After the war, French troops were based there until the 1990s.

For him, it is a reminder that the euro is not just an economic pact but also a glue ensuring Europe’s peaceful future.

Polls have shown a majority of Germans, fed up with their profligate neighbors, are against further bailouts or a fiscal union. One recent poll found more than half of Germans want Greece kicked out of the euro zone, with more than 20 percent saying Italy, Ireland and Portugal should also get the boot.

Boehme, however, said he believes that Germans will ultimately agree to back the debt of their neighbors because it makes good business sense.

Germany’s exports to its euro partners have soared over the past decade, as countries such as France, Italy and Spain used their newfound buying power to scoop up everything from BMW sedans to Siemens power plants.

Since the 1990s, Boehme has worked at Solar-Fabrik, a Freiburg company making solar panels. The industry did bang-up business in Germany’s domestic market during the 2000s. But competition from the Chinese and a reduction of government incentives for alternative energies have curtailed recent sales in Germany. Now, the company is relying on exports for 65 percent of its sales. Its No. 1 destination: France.

“Do I agree with the Greeks retiring at age 50? No, I don’t,” he said. But, he added, “it seems to me that Germany must do whatever is possible to make sure the euro works.”