Officers discovered gas cylinders with detonators attached in the hallway and outside a building in the city's western 16th district in the early hours of Saturday morning.
The five suspects, all in their 30s, remain in custody, a source close to the investigation told AFP today.
Some are known to police for belonging to a radical movement, the source added.
Speaking to Franceinfo radio today, Interior Minister Gerard Collomb revealed that one of the arrested men was on a police terror watchlist.
More From This Section
French lawmakers in the lower house of parliament were set to vote later today on a new counter-terrorism law that rights groups and UN experts have criticised for giving too much power to police and local government officials.
In Saturday's incident, a resident alerted police after finding two gas cylinders around 4:30 am (0230 GMT) in his building in the Porte d'Auteuil neighbourhood, a source close to the probe said.
A mobile phone attached to the cylinders is being investigated as a possible detonator, a security source told AFP.
A total of 241 people have been killed in a wave of jihadist attacks in France since 2015.
On September 12, Collomb said that 12 planned attacks had been foiled since the beginning of the year.
Three suspected women jihadists were arrested in September last year after the discovery of gas cylinders in a car near Paris's Notre Dame Cathedral.