Duchaussoy will have the difficult mission of restoring the image of French football and the credibility of its federation following France's World Cup debacle.
"South Africa left the image of a France team in crisis, both morally and sportingly. Today, it is on the way of reconstruction and even redemption", he said prior to the vote.
The 1998 champions left this year's World Cup with just one point and one goal from the group stage. The team created a scandal by boycotting a training session in support of Chelsea striker Nicolas Anelka, who was sent home for insulting then coach Raymond Domenech.
The French FA has been hit by two departures in the last three weeks. General director Jacques Lambert resigned in November to take a management position in the Euro 2016 organising committee while former France defender Lilian Thuram quit his post as a council member last week.
The Federation is also locked in a battle with Domenech who is seeking 2.9 million euros in compensation for unfair dismissal.
Duchaussoy, 67, had been deputising for former president Jean-Pierre Escalettes who resigned in late June.
He was the only candidate after vice-president Noel Le Graet stepped down on Friday.
