The three - a 16-year-old girl, a man of 20 and a 33-year-old - were detained for a further 48 hours, sources said on Sunday.
Since the investigation is terror-related, they can be detained for up to six days.
On Saturday evening they were transferred from the south of France, where they were arrested, to the headquarters of France's anti-terrorist police at Levallois-Perret, just outside Paris.
A fourth man arrested on Friday was released after being cleared of all suspicion.
Investigators found bomb-making instructions and material in the flat of the 20-year-old man, whose first name is Thomas, and believe the group had plans for an attack but have not established where or when.
But analysis of their phones and computers has shown some potential targets, including the Eiffel Tower, a source told the AFP news agency.
Plans to marry
Thomas was placed under house arrest for a year in the aftermath of the November 2015 Paris attacks because of an unsuccessful attempt to go to territory held by the Islamic State (IS) armed group in Iraq and Syria.
He and the girl, a Muslim convert whose first name is Sarah, had announced plans to marry on social media.
She too had hoped to go to IS-held territory and had sworn allegiance to the group in a video.
They both appear "very radicalised", the sources say.