FFF chief Fernand Duchaussoy (pictured) and France coach Laurent Blanc denied any knowledge of such plans in separate news conferences on Friday.
Duchaussoy said there would be an internal investigation at the Federation, however, to check claims from French website Mediapart that some FFF officials wanted the quotas.
Duchaussoy flatly denied that "instructions, orders" were given by the ruling body.
"But then, in an informal discussion... I cannot be everywhere. There will be an investigation", he added.
"What happened in a meeting, behind a door or in the corridors... I cannot vouch for everyone working at the federation. But I am confident (that there was no wrongdoing)," he added.
National Technical Director Francois Blaquart said that the FFF's concern was on young players with dual nationality eventually dropping France for their country of origin.
"Do we accept this situation? Is it our role to groom players for other countries?" Blaquart, who was targeted by Mediapart's allegations, told the same news conference.
"No such project has been revealed to me. It's a lie," Blanc told a separate news conference in Bordeaux on Friday.
"You cannot have quotas in football. It does not exist. Football is made of diversity."
Blanc, who won the 1998 World Cup with a team dubbed 'Black-Blanc-Beur' (Blacks, Whites and Arabs) by French media, has often raised the problem of dual nationality players mentioned by Blaquart.
"It is a shame to accuse our club like this," Marseille sports director Jose Anigo told the French champions' website.
Marseille coach Didier Deschamps, who captained the France team that won the World Cup in 1998, told a news conference: "I know Laurent Blanc. We played together in a multiracial team. We were proud of that identity and we still are."
Lyon said on their website: "Olympique Lyon deny as strongly as possible the Mediapart allegations."
"These events show that racism has been trivialised on all levels of our society, from the Elysee (home to the French president's office) to the FFF," Les Verts said in a statement.
