One young Muslim man told al Jazeera: "The problem with the way Sarkozy created the CFCM is that he wanted to have control over a body tasked with organising Muslims.
"Just because we're Muslims, does that mean we're going to create underground mosques and be extremists?"
Chems Eddine Hafid, a lawyer who works for the council, has a different interpretation: "What are we trying to do? To try to organise the Muslims of France in the framework of secularism, within the framework of the laws of the state and to make sure Muslims have their place on par with other communities.
"There's no problem. We're here to live together and, of course, as Mr Sarkozy said, to bring Islam up from underground."
Haj Thami Lbrez is the leader of an organisation that joined the council, but he has become more critical of what he says is a body crippled by malfunction and interference not only from the French government but from abroad.
His movement has told its supporters to vote against Sarkozy in the second round of France's presidential elections.
Azouz Begag, the former delegate minister for equal opportunity, resigned from Dominique de Villepin's government on April 5 in order to lend his support to Francois Bayrou, the centrist presidential candidate.
He told Al Jazeera: "While apparently united against Sarkozy ... Muslims of France are also sceptical of an establishment they say failed them many times."