A Palestinian mob surrounded the convoy as it headed for Beit Hanoun in northern Gaza, Maariv said.
Protesters held posters calling for Alliot-Marie to leave, some of them threw shoes at her vehicle and one briefly jumped on top of it, Agenzia Giornalistica Italia reported.
Hamas police eventually dispersed the crowd and allowed the convoy through, Haaretz said.
The Palestinian protesters, mainly relatives of Palestinian prisoners incarcerated in Israel, were angry about statements Alliot-Marie made at a meeting with the parents of Israeli soldier Gilad Shalit on Thursday, Maariv said.
The French foreign minister told Aviva and Noam Shalit in Jerusalem their son "has been held hostage for over four years," Maariv said. She said Shalit continues to be held in isolation and France is doing everything possible to secure his release.
Shalit has dual Israeli and French citizenship.
The soldier was on duty near the Gaza border in June 2006 when he was abducted and taken to the Gaza Strip. He has been held incommunicado ever since.