Special policing powers used under the state of emergency -- such as house arrests and the right to raid houses without judicial oversight -- are currently based on an ordinary law which can be challenged at the constitutional court.
In the wake of the Paris attacks that left 130 dead, President Francois Hollande called for the emergency powers to be protected from litigation by placing them in the constitution.
"The threat has never been higher," Prime Minister Manuel Valls told reporters following a meeting of government ministers today.
The constitutional reforms must now be passed by a three-fifths majority in the upper and lower houses of parliament, where debates will start on February 3.
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Valls said the latest figures showed more than 1,000 people had left France to join the jihad in Syria and Iraq, of which an estimated 148 had died and 250 returned.
"Radicalised individuals from numerous countries join Daesh (the Arab acronym for the Islamic State group). There are many French speakers and we know that fighters group themselves according to language, to train and prepare terrorist actions on our soil," he said.
There are an estimated 3.5 million French people with a second nationality in the country.
Justice Minister Christiane Taubira had voiced doubts over the citizenship clause and wrongly stated it would be dropped. She said on Wednesday that the final word went to Hollande.
"Everyone has a right to their doubts, their queries, their questions," Valls told reporters when asked about Taubira's position on removing citizenship.
There has been criticism from civil rights groups over the violence of police raids, cases of mistaken identity and people losing their jobs because they were placed under house arrest.
An environmental activist has already challenged the right to conduct house arrests, although the court ruled yesterday that they were allowed under state of emergency rules.