The embassy contacted its wardens asking them to convey the new warning to French nationals, the sources said, adding that the advice was precautionary and not based on any specific threat.
Two Kuwaiti security officers were killed and four others wounded in two gun fights with suspected insurgents on 10 and 15 January.
Two suspects, including a Saudi, were also killed in the clashes.
The French warning followed an advisory from the US embassy on Thursday warning of the danger of more unrest, saying residential complexes for Westerners could be targeted.
The British embassy also warned its citizens of a continued threat to Westerners in Kuwait.
Foreign embassies have warned
their citizens to avoid malls
Kuwait, which served as the main launch pad for the US-led invasion of Iraq in March 2003, is home to about 12,000 Americans and 9000 Europeans, mostly Britons.
Kuwaiti security forces have arrested about 15 suspected Islamist insurgents, according to Interior Minister Shaikh Nawaf al-Ahmad Al Sabah, but an unspecified number, including the group's spiritual leader, are still at large.
Al Sabah acknowledged last week that the insurgents belonged to an "organised group", but the country's national guard chief, Shaikh Salim al-Ali al-Sabah, said some of the group were members of al-Qaida.
The authorities say they have seized large quantities of arms, ammunition and explosives since the clashes.