This is the first attack on a foreign mission since militants stormed the United States consulate in Benghazi in September.
The Libyan foreign ministry called the attack in Tripoli a "terrorist" incident.
An Agence France-Presse correspondent at the site said the wall surrounding the property was destroyed and the embassy building extensively damaged. Two cars parked near the embassy were also destroyed.
The explosion occurred around 7am.
A French source confirmed an attack against the embassy and said one guard was seriously wounded and another lightly hurt.
The mission is located in a two-storey villa in the upmarket Gargaresh area.
"We heard a loud blast at 7am. It was a big mistake to site the French embassy in our neighbourhood," said a local resident.
France condemned the "odious" attack.
"In liaison with the Libyan authorities, the services of the state will do everything to establish the circumstances of this odious act and rapidly identify the perpetrators," Foreign Minister Laurent Fabius said.
The impact of the explosion also severely damaged two villas near the embassy, while windows of a shop 200 metres away were blown out.
The street in front of the mission was flooded with water, apparently from a pipe ripped by the blast.
There was no immediate information on who carried out the attack or what the motives were.
France, under the presidency of Nicolas Sarkozy, led air raids against the forces of then Libyan ruler Muammar Gaddafi in 2011 after a rebellion against his regime erupted.
The operation, under a United Nations resolution aimed at protecting civilians in Libya, helped defeat and topple Gaddafi's regime, and the dictator was killed in October 2011 after an eight-month conflict.
Since Gaddafi's fall, Libya has been plagued by persistent insecurity, especially in the region of Benghazi, which has been hit by bombings and assassinations that has forced many Westerners to leave the eastern city.
In September an attack on the US consulate killed four Americans, including ambassador Christopher Stevens.
The envoy died when the consulate was attacked by an armed mob protesting against a low-budget anti-Islam film produced in the United States, which mocked the Prophet Muhammad.
The movie, Innocence of Muslims, triggered widespread anger and violent protests in several Muslim countries across the world.
The Benghazi attack sparked a ferocious backlash from Republicans during the 2012 US presidential race, who alleged that President Barack Obama's administration sought to cover up details of the incident.
The violence in Libya is often blamed on radical Islamists persecuted under Gaddafi and who now want to settle old scores, while security remains the prerogative of militias in a number of important areas.
Adding to the woes is a regional context marked by the conflict in Mali where the French army intervened at the request of the authorities in Bamako.
Armed jihadist groups hurt by the French intervention in northern Mali had threatened retaliation by attacking French interests. – AFP