The funds' BNP exposure represented 24 percent of their total $163 billion holdings in French debt last month and was slightly less than the $39.5 billion at the end of April, JPMorgan analysts said.

"Given the timing of the negative headlines in late May, we did not see a significant retrenchment in the amount of BNP Paribas holdings at the end of the month," the analysts wrote in the report.

The bank, France's biggest, had a broad investor base with 18 fund families owning its securities at the end of last month, the analysts said.

U.S. authorities are investigating whether BNP evaded U.S. sanctions against certain countries between 2002 and 2009. Sources familiar with the matter say the authorities are trying to establish whether the bank removed identifying information from wire transfers so they could pass through the U.S. financial system without raising red flags.

(Reporting by Richard Leong)