The first incident took place on June 17 when Karim Djaziri “shoved” a L’Equipe reporter, the newspaper said.
On the night of July 5, hours after France’s quarter-final loss to Germany, Djaziri had a run in with another reporter, “striking a blow before insulting him and threatening him in an explicit way”, the paper wrote.
The paper also claimed a man purporting to be a “friend” of Benzema and Djaziri “slapped” a third L’Equipe reporter.
Djaziri refused to comment on the allegations when contacted by AFP.
Benzema, the 26-year-old Real Madrid forward, scored three times to help France out of the World Cup first round as group winners.
Didier Deschamps’ side then saw off Nigeria 2-0 in the last 16 before going down 1-0 to Germany in the quarter-finals.