In the capital, Tripoli, protesters stormed parliament to demand the dissolution of the General National Congress (GNC), shooting and wounding two lawmakers and beating others.
Many Libyans blame the GNC and the government for the chaos that persists three years after Muammar Gaddafi’s overthrow.
A security official named the Frenchman killed in Benghazi as Patrice Real, who worked for a company upgrading a large hospital. “He was killed with three shots,” the official said.
The French Foreign Ministry condemned the killing as “odious and cowardly” and called for its perpetrators to be identified.
In other attacks in Benghazi, a city plagued by bombings and assassinations, gunmen wounded an Egyptian grocery worker and a Libyan police officer, a security source said.
A week ago, police found the bodies of seven Egyptian Christians shot dead execution-style on a beach near Benghazi, a hotbed of Islamist militancy. No group has claimed responsibility for the killings.
Gunmen killed an American schoolteacher in the city in December while he was out jogging.
Most foreign consulates have closed in Benghazi, where several oil firms have offices, and some airlines have stopped flying there since the US ambassador and three other Americans were killed in an Islamist militant onslaught in September 2012.
Western diplomats fear the violence in Benghazi will spread to Tripoli. A British man and a New Zealand woman were shot dead on a beach 60 miles (100 km) west of the capital in January.
In Sunday’s attack on parliament, dozens of protesters burst into the building, assaulting and wounding several lawmakers, GNC spokesman Omar Humeidan told Al-Nabaa television.
Protesters shot and wounded two lawmakers when they tried to leave the building, assembly member Nizar Kawan told Reuters.
Halima Al-Warfalli, a deputy from Benghazi, said some of the young protesters had carried knives. “They came inside the building, beat some people and damaged furniture,” she said.
GNC members agreed to hold elections later this year after a public outcry over their attempt to extend the mandate of the transitional assembly, which expired on February 7.
Libya’s weak government and army are struggling to control well-armed former anti-Gaddafi rebels and Islamist militias.