'We can no longer borrow dollars. U.S. money-market funds are not lending to us anymore," a bank executive for BNP Paribas, who declines to be named, told me last week. "Since we don't have access to dollars anymore, we're creating a market in euros. This is a first. . . . We hope it will work, otherwise the downward spiral will be hell. We will no longer be trusted at all and no one will lend to us anymore."

He's not the only one worried. France's three biggest banks have...