His decision comes follows mounting criticism of his presidency after France's World Cup campaign which saw Les Bleus eliminated after the group stage with just one goal and one point from three matches.
The team also hit the headlines after striker Nicolas Anelka was sent home for allegedly insulting coach Raymond Domenech and the players "went on strike" by refusing to attend a training session.
In a short statement released on the Federation's website on Monday, Escalettes said he had spent the past couple of days thinking about his future and took his share of the responsibility for what had happened.
"After a weekend of reflection during which I consulted my colleagues, staff and my family, I consider it my duty to resign," he wrote.
"I accept my share of responsibility," he continued. "It's a decision taken mainly by my wish to preserve and help the evolution of the institution I've served with passion for several decades."
Escalettes has been president of the FFF since 2005 and was seen as instrumental in solving its financial problems and leading France's successful bid to host Euro 2016.
But he also faced criticism for leaving Domenech in charge after France failed to make it past the group stage of the Euro 2008 finals and later struggled to qualify for the World Cup in South Africa.
The 75-year-old's tenure as FFF president had been due to run until 2012.
Last week after what she called the "disaster" of France's World campaign, the French sports minister Roselyne Bachelot said in an interview on national radio that although she didn't want Escalettes to resign she considered in an "unavoidable consequence."
Last week after what she called the "disaster" of France's World campaign, the French sports minister Roselyne Bachelot said in an interview on national radio that although she didn't want Escalettes to resign she considered it "unavoidable."
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