The former World Cup-winning captain Didier Deschamps is the favourite to be the new France coach after Laurent Blanc turned down a new contract offer to stay.
Blanc stepped down after a European Championship campaign that ended in the quarter-finals and with his players again being questioned about their behaviour.
Blanc informed the French Football Federation of his decision following lengthy negotiations with the federation's president, Noel Le Graët, on Thursday.
Deschamps played 103 matches for France and is set to leave his role as Marseilles manager after seeing them finish a disappointing 10th last season. He has made no secret of his desire to coach France. He was France's captain when they won the 1998 World Cup and Euro 2000 – the national team's last major trophy – and would be a popular choice.
Le Graët, however, had hoped Blanc would stay on. "Laurent Blanc contacted the federation president on Saturday to tell him of his decision not to accept the renewal of his contract as national team coach," the federation said in a statement.
Blanc was reportedly unhappy he had not been offered a contract extension before Euro 2012 started, with the federation preferring to wait and see how the team performed. France lost their final group match to 2-0 Sweden, who still finished last in Group D. That put them into a quarter-final against Spain, who beat them 2-0.
France's Euro 2012 campaign was tainted by tensions among the players following a heated changing room bust-up immediately after the loss to Sweden, while midfielder Samir Nasri was also embroiled in an expletive-laced exchange with a French journalist.
Those incidents may have influenced Blanc's decision.
He took charge of France in July 2010 following the World Cup debacle in South Africa, where the players went on strike in protest against then-coach Raymond Domenech.
Blanc's tenure was fairly successful and he rebuilt the team following the shambles of the Domenech era. Under Blanc, France reached the quarter-finals of a competition for the first time since the 2006 World Cup, drawing a line through the failures of Euro 2008 and the 2010 World Cup finals, in which France failed to win a single game under Domenech.
Blanc lost his first two games in charge, but the team then embarked on a 23-match unbeaten run before losing to Sweden and Spain at Euro 2012. Altogether, France lost only four out of 27 matches under Blanc.
Having led Bordeaux to the French title in 2009, Blanc may return to club management. He had previously been linked to the vacant manager's position at Tottenham.
The former France manager Michel Hidalgo said: "It's a shame that Blanc is not staying .It's hard to understand, but it is Laurent Blanc alone's decision."
Hidalgo, who guided France to their first trophy at the 1984 European Championship, thinks Deschamps would be the ideal choice.
"At 43 years old, he's ready for everything. He has good qualities," Hidalgo said.
The former France left-back Bixente Lizarazu was also disappointed by Blanc's decision, saying: "A big surprise, a big waste. I think Laurent Blanc had all the cards in hand to decide to carry on, with the challenge of the 2014 World Cup in Brazil.
"Maybe it was down to the discussion with Noel Le Graët. Both of them were waiting to see if there was a desire to work together and, since both seem to be very, very stubborn, with a strong character, neither of them made the first step. It's a bit like in a relationship where you have to say 'I love you' first. No one says it and you split up."
Blanc restored the pride of the national team after it hit rock bottom at the last World Cup, with the players shocking fans back home and causing public outcry by going on strike at a training session in protest after striker Nicolas Anelka had been sent home for insulting Domenech.
The task appeared even more difficult for Blanc when France opened their Euro 2012 qualifying campaign with a 1-0 loss at home to Belarus. Things picked up quickly, however, and confidence was boosted by impressive wins against England, Brazil and Germany in friendlies.
Against Spain at Euro 2012, however, Blanc received criticism for choosing a negative line-up that featured two right-backs.
Striker Karim Benzema received no service and failed to score in four matches at Euro 2012. The abject performance against Spain came just days after an equally poor showing against Sweden, perhaps showing the limitations of the team and how far Blanc could take it.
The row in the changing room that followed the Sweden match also showed Blanc that the players are still difficult to handle, and that another two years in charge would mean having to address tensions within the squad amid constant media exposure.Reuse content