The Real Madrid forward scored in the second half of his side's 6-0 victory at the Parc des Princes in Paris.
"I have managed to score the goal that had weighed a little on my mind," Goal.com quotes him as saying.
"I thank all the team who have been behind me. It was nice to be supported by the public. There is another game on Tuesday [against Finland] and we will need the win."
Prior to Friday, Benzema had last scored for France against Estonia in June 2012.