BY GRÁINNE MCCARTHY AND MARTINE PAUWELS

PARIS—BNP Paribas said Thursday it is selling a 28.7% stake in French real-estate company Klépierre SA to U.S. shopping mall giant Simon Property Group, a significant step in efforts by France’s largest listed bank to shore up its capital levels to meet new solvency regulations.

BNP Paribas said the sale, at €28 a share, will generate an approximate capital gain of €1.5 billion ($2.0 billion).

BNP Paribas and its large French peers are busily shrinking the size of their balance sheets after being hurt since last summer by the euro zone debt crisis. All of them are working to escape …