French president Francois Hollande has ordered security step up around public buildings and transport areas because of military operations in Africa.
He was responding to the risk of Islamist attack after French forces attacked militants in Mali and Somalia.
A pilot was killed as air strikes were launched on Malian rebels.
In Somalia, two French soldiers were “sacrificed” in a raid to free a French hostage who was eventually killed.
His remarks came within hours of one of the Islamist groups targeted by French military action in Mali threatening reprisals against France.
An Ansar Dine spokesman told Reuters news agency, there would be consequences for French citizens throughout the Muslim world.
The operations in Mali and Somalia were launched within hours of each other but were “totally unconnected”, according to government officials.
French troops were deployed in Mali on Friday after the army lost control of a strategically important town to Islamists who were advancing south. The rebels took control of a huge swathe of northern Mali last April.
The African Union plans to refer the situation in Mali to the United Nations Security Council so that it can create a framework for tackling the worsening crisis there, a diplomatic source close to the AU president said on Wednesday.
Mali, once regarded as a fine example of African democracy, collapsed into chaos after soldiers toppled the president in March, leaving a power vacuum in the north that enabled rebels to take control of nearly two-thirds of the country.
A regionally backed transitional government has been set up in Bamako to organise new presidential elections within a year, though supporters of the ruling military junta oppose the plan.
“The African Union will go to the Security Council and then it will be up to it to find the right format for a resolution and if it deems military support necessary,” said the source close to Thomas Boni Yayi, the Benin president and head of the African Union.
He said it was not clear when the issue would be taken to the United Nations.
An agreement between northern Mali’s MNLA Tuareg rebels and the al Qaeda-linked Islamist group Ansar Dine to create an Islamic state in northern Mali’s Azawad desert has hit trouble over how strictly to impose sharia, Islamic law.
The separatist MNLA wants a moderate form of sharia, while Ansar Dine would like to impose a more hardline version, using punishments such as the amputation of hands and heads for certain crimes.
The West African group ECOWAS said it rejected the idea of a separate Islamic state in northern Mali, and new French President Francois Hollande urged African leaders on Tuesday to ask the U.N. Security Council to help restore stability in the region.