The blast in Tripoli destroyed the embassy’s ground-floor reception area and perimeter wall, as well as damaging neighbouring homes and shops.
French President Francois Hollande called on Libya to act swiftly over this “unacceptable” attack.
It is the first major attack on a foreign embassy in the Libyan capital.
Tuesday’s explosion happened shortly after 07:00 (05:00 GMT) in a smart residential area of Tripoli.
One of the embassy’s guards was severely injured while the other suffered lighter injuries. Several residents were also slightly hurt.
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It was a big mistake to site the French embassy in our neighbourhood”
Local resident
One young girl suffered a spinal cord injury and was being transferred to neighbouring Tunisia for treatment, her father told the BBC.
The blast took place in a small side street and left a scene of devastation, the BBC’s Rana Jawad in Tripoli reports.
As well as extensive damage to the embassy building and perimeter wall, two nearby homes were badly damaged and others affected, while the windows of a shop were blown out and two parked cars were burnt out.
Many neighbours who gathered in the street to survey the damage were shaken and upset by what had happened, our correspondent says.
They told her that there was a lack of proper policing for such a potentially high-profile target.
“It was a big mistake to site the French embassy in our neighbourhood,” a local resident said.
President Hollande said the attack had targeted “all countries in the international community engaged in the fight against terrorism”.
“France expects the Libyan authorities to shed the fullest light on this unacceptable act, so that the perpetrators are identified and brought to justice,” he said.
French Foreign Minister Laurent Fabius – who has arrived in Libya to see for himself the damage – said French officials would work closely with the Libyan authorities to find out who was responsible for what he called an “odious act”.
Libyan Foreign Minister Mohammed Abdel Aziz condemned the bombing as a “terrorist act”, but did not speculate on who might be behind it.
No group has yet claimed responsibility for the attack.
French embassies across northern Africa have been on high alert since France sent in troops to help fight an Islamist insurgency in Mali in January.
France, under Nicolas Sarkozy, was at the forefront of Nato-led air strikes in 2011 that helped rebel forces topple long-time Libyan leader Muammar Gaddafi.
The US consulate in the eastern city of Benghazi was attacked by armed men in September 2012, leading to the killing of ambassador Christopher Stevens and three other American officials.