Carrefour SA takes its name from the French for crossroads. But after 10 years of decline, and a miserable six months in which management bungled two major strategic moves, the world's No. 2 supermarket operator may be driving into a dead end.

Shares fell by half in the year to Aug. 30, to as low as €16.68 on Aug. 11, near a 15-year low. Turnaround talk is giving way to whispers that investors, including No. 1 shareholder Colony Capital LLC of Los Angeles, are preparing the company for breakup. "I think signs are increasingly pointing to a breakup, particularly if Carrefour exits Brazil," says Natalie Berg, co-global research director at London's Planet Retail Ltd. "There would be buyers for Carrefour's emerging-markets operations, on a piecemeal basis, leaving a European operation that could be attractive to private equity."

Carrefour's rivals are circling. Wal-Mart Stores Inc., the world's largest retailer and Brazil's No. 3 player with 12% market share, has hired advisers, including UBS, to explore a bid for Carrefour's Brazilian unit. Wal-Mart's own performance in fast-growing Brazil has been lackluster. Carrefour controls 14% of the supermarket sector by sales, second to Grupo Pão de Açúcar, with 18% share.

Carrefour would almost certainly be worth more in pieces than its market capitalization of €12.85 billion ($18.54 billion). Operations in Brazil, Argentina, Colombia and China might fetch twice as much as their current implied value when untethered from Carrefour's sluggish European business, analysts say. Pão de Açúcar's market capitalization is 5.4 times forecast Ebitda for 2011 of 2.44 billion reais ($1.52 billion), a figure based on an extrapolation of half-year results. Carrefour trades at 2.9 times its €4.4 billion of forecast Ebitda for 2011.

Selling its emerging-markets assets could add €3 billion to €4 billion to Carre­four's current value, Bank of America Merrill Lynch analysts say. A generous takeover premium could push that even higher. In late 2010 French rival Casino Guichard-Perrachon SA paid 13 times Ebitda for Carrefour's Thai unit.

Carrefour insists it remains committed to key emerging markets and a plan to turn around its underperforming French operations. "Carrefour in Brazil is not for sale, and there is no negotiation with Wal-Mart," company CEO Lars Olofsson said in August.

The problem for Olofsson, who joined from Nestlé SA in 2009, is that he almost surely doesn't have the final say.

Blue Capital Sarl, an investment partnership between Colony Capital and Groupe Arnault SAS, the investment vehicle of French billionaire Bernard Arnault, holds the real power. The group owns 14% of Carrefour and controls 20% of its voting rights. It more than anyone has suffered from Carrefour's sliding value after paying €2 billion at an average of about €45 per share in 2007, leaving it with a paper loss of over €1 billion.

Speculation that Blue Capital may be ready to put Carrefour's emerging-markets business on the block was stoked by a recent management shuffle. In August Pierre Bouchut, formerly Carrefour's finance head, was named head of emerging markets, replacing Thierry Garnier. Bouchut, unlike Garnier, is considered to be close to Blue Capital. "It is true that if you're going to sell a unit, you want a numbers man in charge of it," says a Paris-based fund manager. "Then again, [Bouchut] would also be the right man to sort out any ongoing accounting problems." Last year Carrefour discovered a hole in its Brazilian accounts that prompted a €550 million profit warning.

Blue Capital has already shown that it will intervene at Carrefour. It was behind the ousting of Olofsson's predecessor, José Luis Duran, in 2008, following disagreements over strategy and just three years after his appointment. Blue Capital took the opportunity to install three of its representatives on the board.

Blue Capital has said it will give Olofsson time to implement a turnaround. But how much patience, and confidence in Olofsson, does it have left?

In the past six months, his credibility has been battered by two misadventures. In March, under pressure from Blue Capital, he announced plans to spin off the real estate division, only to shelve the estimated €10.4 billion IPO two months later after a management and shareholder backlash.

In July he abandoned plans to merge Brazilian operations with Pão de Açúcar after badly misjudging the ability of Casino -- Açúcar's biggest shareholder -- to block the move.

At the end of August, Carrefour said current operating income was likely to dip 15% in 2011, blaming worse-than-expected results from its French hypermarket operations.

Olofsson hopes to transform those hypermarkets into so-called Carrefour Planets -- megashops that sell groceries, electronics, sporting goods and furniture. Sales at these stores posted double-digit growth, Carrefour said in July.

Olofsson's future probably rests on Blue Capital's faith that he can pull off the strategic shift. If that faith is lost, then Carrefour itself may well find it has reached a final crossroads.