Bernard was reported to be one of four candidates in the frame for the top job at the German retailer, following his departure from the French world number two retailer in February.
KarstadtQuelle chief Christoph Achenbach was ousted from his position earlier this month, days before the retailer announced a loss before tax of Eu191 million (£130.1 million) for the financial year, compared with a profit of Eu9 million (£6.1 million) a year earlier.
Karstadt chief financial officer Harald Pinger is manning the helm at the retailer until a permanent chief executive is found.
Bernard resigned from Carrefour following a management re-organisation that involved operations and strategy being separated into two management teams.
Former Marks & Spencer chairman Luc Vandevelde was appointed as president of the strategically focussed supervisory board at the retailer.