HSBC Holdings PLC said a former employee stole data on about 24,000 accounts in its Swiss private bank that wound up in the hands of French authorities, the latest case to highlight the complications that arise when stolen bank information ends up in the custody of governments eager to chase tax cheats.

The HSBC situation involves a former information-technology employee, Herve Falciani, who is alleged to have stolen the data in 2006 and 2007 and then attempted to sell them to several governments. Confronted with theft allegations by HSBC in December 2008, Mr. Falciani, a dual French-Italian national, fled to France. A month later, French authorities raided his house there and confiscated the data.