For more than a century, Geneva has provided wealthy French families a convenient and safe place to stash their money. Switzerland’s political neutrality, stability, and tradition of bank secrecy have kept their fortunes beyond the reach of warring powers and the most determined tax collectors, even though Geneva is less than 3 miles from the French border. In turn, French funds have helped build the city into a showpiece for Gallic culture—and the world’s largest concentration of wealth managers.

Those long-standing ties are unraveling as France toughens its tax laws and Paris prosecutors investigate UBS (UBS), Switzerland’s largest lender, and HSBC Holdings (HSBC) to find out whether they helped clients hide wealth in Swiss accounts. Already bruised by battles with the U.S., Geneva bankers are pressing French customers to “regularize,” a polite way of saying they must declare hidden funds to French tax authorities. Failure to do so will result in the closing of their accounts, clients have been told.

Banks are “very scared,” says Rémi Dhonneur, a lawyer at Kramer Levin Naftalis & Frankel in Paris. “Clients are being kicked out or pushed to regularization.” The French have at least €250 billion ($340 billion) in foreign accounts, and more than half may be undeclared, says a Geneva-based banker who asked not to be named, saying the figures were supplied confidentially by a consulting firm. Geneva holds 80 percent to 90 percent of that money, according to tax lawyers interviewed by Bloomberg.

France offered last June to reduce fines on unreported wealth held abroad to encourage voluntary declarations. The program has yielded €764 million in taxes from 1,260 cases examined so far, the French government said in late May. A law adopted in December gives French authorities more power to go after suspected tax cheats and calls for a €2 million fine and a sentence of as many as seven years for bankers, wealth managers, advisers, and lawyers who organize tax fraud. Judicial authorities are investigating UBS after France’s banking regulator fined the bank €10 million last year for deficient controls against tax fraud and illegal sales practices. The probe into HSBC, which also began last year, concerns allegations that the bank helped French clients avoid taxes. The government has built its case from a list of clients leaked from the bank’s Geneva unit by Hervé Falciani, a former software technician at HSBC.

Since 2009, U.S. tax probes have cost Switzerland’s biggest banks, UBS and Credit Suisse (CS), more than $3 billion in penalties and felled the country’s oldest bank, Wegelin & Co. About a dozen other banks are under investigation for allegedly helping wealthy Americans cheat on their taxes. Credit Suisse became the first bank in more than a decade to admit to a crime in a U.S. courtroom when it pleaded guilty to a decades-long pattern of helping Americans evade taxes in offshore havens and agreed to pay $2.6 billion in penalties. The resolution of that case cleared the way for other Swiss banks to settle their own U.S. tax disputes. Many of these banks, including Pictet & Cie. Group and HSBC’s Swiss unit, are the same ones putting pressure on their French clients to come clean.

Swiss banks “are doing as much as they can” to guide French clients through their country’s “costly” and “complicated” disclosure program, Patrick Odier, chairman of the Swiss Bankers Association and senior partner at private bank Lombard Odier, said in an interview with L’Agefi newspaper on May 8. Neither Lombard Odier nor Pictet would comment on policies toward French account holders. Credit Suisse “is asking clients to regularize their tax situation,” spokesman Jean-Paul Darbellay wrote via e-mail.

For most clients of Paris-based lawyer Lea Falcon, Geneva still has appeal—if not for secrecy, then for stability. She points to Cyprus, where the government seized bank deposits to qualify for a bailout from the European Union last year after its financial system nearly collapsed. “They still trust Switzerland more than they trust France,” Falcon says. “They are scared their assets might be taken by the state if they are with a local French bank, following the example of Cyprus.”