FRANKFURT — It is getting harder and harder to find free parking for large sums of euros.

In a battered regional economy, the search for safety has become so desperate that some European investors are willing to pay for the privilege of lending to France — a country dealing with economic stagnation, political gridlock and a tough business climate. Investors might not expect their money to grow in France, but they trust that it won’t disappear.

The yield on French government two-year bonds turned negative on Monday, before edging back into positive territory Tuesday. Yields on some German debt, another perceived bastion of safety, have been below zero off and on since last month. In addition, banks have been willing to pay their most solid peers to store their money overnight.

This upside-down financial world, in which lenders pay borrowers to take their money, is the result of a decision by the European Central Bank in June. The E.C.B. effectively imposed a penalty on banks that park money in the central bank’s vaults. The radical move was an attempt to stoke the economy by forcing banks to lend to businesses and consumers.

But the strategy has not worked, one reason the central bank is under increasing pressure to try something else when it meets on Thursday — limited though its remaining options might be.