Tuesday's Le Parisien newspaper named some of the many districts affected, which it claims include Saint-Tropez in the south and the department of Seine-Saint-Denis north of Paris.
The problems stem from low-interest loans that were taken out on the condition that if the euro-franc exchange rate fell below a certain level, rates would become progressively higher.
The Swiss franc has fallen in ten years from a rate of around 1.5 francs to the euro to a close on Monday of 1.1 francs. At its strongest, in October 2007, the euro bought almost 1.7 francs.
Le Parisien claimed that some of the interest rates have now soared to 20 percent. Some local authorities have decided to take legal action to try to avoid the punitive charges.
"We contest the legality of these loans where the interest rates and the penalty calculations are not clearly stipulated," lawyers working for the mayor of Saint-Cast-le-Guildo in the northern Brittany region told Le Parisien. The town is taking action against the bank Dexia, which sold it the loan.
"We are bound hand and foot," said the mayor, Jean Fernandez. "I'm a maths teacher and even I find it impossible to understand the formula that Dexia put in this contract."
The newspaper claimed that many more local authorities, emergency services, hospitals and other public bodies could be trapped in loans with high interest rates.
The news came on the same day that the Swiss National Bank announced it is setting a minimum exchange rate of 1.2 francs to the euro, although even this rate is unlikely to help many of the struggling loan holders.
See also: Swiss stocks jump on currency peg news