Benzema has not featured for the World Champions since October 2015 after he was allegedly involved in a plot to blackmail France teammate Mathieu Valbuena in a sex-tape scandal.
Les Blues head coach Didier Deschamps has not included Benzema in any squad since the controversial incident.
And FFF president Noel Le Graet admits the former Lyon forward is unlikely to return, regardless if he is found innocent within the ongoing investigation.
"The Valbuena-Benzema affair had another episode last week, but it is still not over," Le Graet told Ouest-France.
"It's been three or four years. It should have been judged much faster and it is rotten for us.
"I have nothing against Karim, he has always behaved well in the [national] team, but I think he is finished with Les Bleus, particularly as he has been out of form for a while."
Benzema recorded 27 goals in 81 caps after scoring on his international debut against Austria 11 years ago.