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Four years ago, when Frederic Jousset and Olivier Duha began trying to persuade European companies to move some of their customer-service operations abroad, they hit a wall of skepticism. It was too risky to move to out-of-the way places like Morocco and Romania, they were told. "It was like evangelizing," recalls Jousset, 34, a former marketing manager at cosmetics firm L'Oréal. But the two men persevered, and today their outsourcing company, Webhelp, is booming. Clients include Tiscali, the Italian Internet service provider, and TF1, France's leading TV station. In June, Webhelp opened its second call center in Rabat, bringing its total workforce to 800, and last week the company announced that its sales were on track to double this year, to j12 million.

But the French government is starting to fight back. It's considering a decree that would require telephone operators talking to French consumers to state their location. Instead of picking up the phone and saying, "Bonjour, this is Marie," the customer-service representative would be required to say: "This is Marie in Rabat." Webhelp worries that such a measure would confuse customers and scare off potential corporate clients. "It could really hurt us," says Jousset. "Over the long term, such protectionist steps never work. But over the next five years it could slow the development."

More than two years after the U.S. began worrying about the export of American jobs to lower-cost countries, Europe has finally woken up to the "offshoring" threat. European companies have been moving some manufacturing facilities abroad for a decade to capitalize on lower wages and to gain access to new markets. But now many firms are asking if they can and should do the same with their service operations — and offshoring is becoming a potent political issue. With international communications costs falling rapidly, customer-service centers are obvious candidates for a move. But more skilled jobs such as computer programming and bookkeeping are also being targeted for export.

With unions fuming over the potential loss of jobs, some European governments are anxious to limit offshoring. "People are scared," Nicolas Sarkozy, the French Finance Minister, told TIME (see President in Waiting?). He wants France to take the lead in discouraging offshoring where possible. As well as the call centers decree, still under discussion, Sarkozy is using tax subsidies to encourage firms to locate operations at home. One beneficiary is the media company Vivendi Universal, which recently won a tax break it estimates to be worth €3.8 billion over the next six or seven years. In exchange, it agreed to create two new call centers — in the northern town of Douai and Belfort in the east. The government isn't saying how many jobs it hopes to keep, but Sarkozy tells TIME that "I'm paid to find a solution." A TIME poll finds that nearly 8 out of 10 French citizens agree with his efforts. Yet experts question whether governments can or should stop private firms from moving jobs to gain competitive advantage.

So far, Europe's biggest job-shifters have been in Britain. Last month, the big insurer Aviva announced it is moving 950 back-office and processing jobs to India and Sri Lanka next year — and laying off 150 workers in Britain as a result. That follows similar announcements over the past year by British financial firms HSBC, Lloyds TSB and Barclays, among others.

Others are trying to catch up. A study carried out last June by German consulting firm Roland Berger polled 500 top European companies, and found that 39% have already shifted some services abroad, and about 20% are planning to do so in the next year. The most alluring feature is the potential savings, largely because of a still-huge disparity in wages between Western Europe and almost anywhere else in the world. The going rate for a skilled computer system architect in India, for example, is about $50,000 per year, compared to $160,000 for the same job in Britain, according to consulting firm Forrester Research.

For all that, there are no reliable statistics about the extent of offshoring. A report last month by the United Nations Conference on Trade and Development (UNCTAD) said that while outsourcing business services is becoming a significant trend, most of it takes place domestically; only 1-2% is done internationally. Others predict a surge. Forrester in August forecast that Europe will lose 1.2 million jobs to offshore service providers by the year 2015. "The fact is that we are in the foothills of a revolution," says Stephen Green, chief executive of HSBC.

Such estimates often overlook important nuances. For one thing, a major beneficiary of the offshoring trend to date has been E.U. member Ireland, which has attracted a influx of investment from U.S. and other companies over the past decade. East European countries are trying to follow Ireland's lead, with places like Prague and Budapest at the forefront. Just over 50% of the European firms surveyed by Roland Berger said they were looking to outsource in other European countries, compared with 37% targeting Asia. That may be driven by language and culture: while British firms easily hire English speakers in India, it's not so easy for German or French companies to find native speakers there.

Many economists and corporate executives call offshoring a natural process that can be of benefit to all. Cost savings help secure jobs at home by improving competitiveness, the argument goes; and offshoring can boost revenue, stimulate exports and prompt the creation of jobs that generate more wealth than is lost. But even the biggest optimists admit that the effects are wrenching for those who lose their jobs. A few unions are trying to mitigate the impact. One success came in Newcastle, England, where Lloyds TSB bank announced a year ago that it was closing a call center and moving around 1,000 jobs to India. The announcement sparked a furor; Newcastle City Council had given Lloyds subsidies to set up the call center two years previously. UNIFI, the union representing about 15,000 of Lloyds' 70,000 staff, called for a strike ballot, and after several months of negotiations, the bank agreed to redeploy people in other jobs where possible. Those laid off when the call center closes next month will get a $3,600 payment toward retraining.

It's a model that the union would like to extend across financial service firms in Britain. "Our priority is to avoid compulsory redundancies," says Rob O'Neill, the union's chief negotiator with HSBC, which has announced plans to cut 7,500 jobs in Britain at the same time as moving 4,000 of them to Asia. O'Neill's union, for one, acknowledges that it's fruitless to fight the offshoring trend as a whole and that it's better to pick the battles carefully. France, by comparison, isn't willing to concede defeat. But, say offshoring's proponents, it's only a matter of time before the French, too, give in.

• PETER GUMBEL | Paris
• Can the French government really stop jobs from going abroad?