PARIS—French prosecutors are targeting several senior BNP Paribas SA officials with a preliminary insider-trading probe related to the lender’s record settlement in the U.S., a person with knowledge of the matter said Tuesday, possibly complicating efforts by one of Europe’s largest banks to draw a line under a difficult chapter.

Paris prosecutors, who opened the preliminary investigation earlier this month, are trying to determine how much senior BNP Paribas directors and top executives knew about the bank’s exposure to...