France have been going through a transitional period under new manager Laurent Blanc after a wretched campaign at the 2010 FIFA World Cup in South Africa, which was blighted by trouble on and off the pitch.
Many though have tipped Les Bleus to be dark horses in Poland and Ukraine next year, citing Greece's shock against-the-odds triumph in 2004 as an example of what can be achieved.
Although a 17-match unbeaten run has raised optimism in France, Leboeuf believes escaping out of a competitive group that includes England, Ukraine and Sweden is the best they can realistically aim for at EURO 2012.
"It's good that France have qualified and we can give major international experience to the players," former Chelsea defender Leboeuf said in an interview on Friday.
"That's the only use we can put the competition to as we don't expect to win. We want to be ready long-term for the World Cup in 2014," added the 43-year-old, in London as an ambassador for English Premier League title sponsor Barclays.
"It's going to be tough as people forget we had to start from scratch," explained Leboeuf, winner of the both the World Cup (1998) and European Championships (2000) with France during his 50-cap career.
"We have done well, but we don't know the value of the team yet. Everyone talks about the past with France, but we lost a lot," he added. "A lot was destroyed with the spirit and the view of the fans towards the team during that World Cup [in South Africa].
"For France, with the likes of Thierry Henry and Zinedine Zidane long gone, getting out of the group stage would be seen as good progress."