Carrefour shares have risen on Thursday amid speculation that Europe's biggest retailer will revamp its management.
Carrefour has seen sales in its French stores slide
French press reported that chairman Daniel Bernard and European head Joel Saveuse would step down. Carrefour shares rose 2.7% to 40.53 euros.
Carrefour would not comment on the reports but said its board was meeting to discuss the firm's "structure".
Sales have been falling at Carrefour's French hypermarkets and it is planning price cuts to attract shoppers.
La Tribune newspaper reported that Carrefour's finance director Jose Luis Duran is set to take over as head of its management board.
Luc Vandevelde, the former chairman of UK retailer Marks & Spencer, is set to become chairman of Carrefour's supervisory board, the newspaper said.
A number of retailers in France are feeling the pinch as sputtering economic growth and concerns about labour market reforms have put consumers off spending.
Sales at Carrefour's French hypermarkets have fallen over the past 18 months. France accounts for about half of the firm's global sales.
Concerns about earnings have hit Carrefour shares, which lost 20% of their value last year and are now half their 1999 price.
To boost investor confidence the firm has promised to sell more than $1bn worth of assets by the end of this year. It has also pledged to deal with its debts, which stand at almost $12bn.
Carrefour, the world's second-largest retailer behind Wal-Mart, had sales of 81.4bn euros (£106bn; £56.2bn) in 2004.
It has more than 10,000 shops in 29 countries.