The vehicle, which had no registration plates, was found with its hazard lights flashing near Notre Dame cathedral on Saturday night.
Police said the car contained six gas tanks and may have been part of a “test run” for a terror attack.
Two people were arrested and taken into custody on Wednesday night, a judicial official said.
The pair were detained near Montargis, around 70 miles south of Paris, a French police source told AFP.
It comes after two people, aged 34 and 29, were arrested at a service station in southern France on Tuesday.
Both were said to have been known to police for having links to extremist Islamists.
The owner of the recovered vehicle was briefly detained and later released, but his “radicalised” daughter is being sought by police, the Paris prosecutor’s office said.
Three other people have also been held and questioned before being released, it added.
The security alert comes after a warning from Paris prosecutor Francois Molins that an increasing number of teenagers have been radicalised in the French capital.
Mr Molins told Le Monde that many of them have “very worrying profiles” and “sometimes terrorist plans that, intellectually, start to be brought to completion”.
He added that 35 minors – 23 boys and 12 girls – are being investigated under preliminary charges, nine of whom have been detained.
France has been under a state emergency since the November 2015 attacks on Paris that killed 130 people and injured hundreds.
Salah Abdeslam, who is thought to have played a key role in the terror plot, kept silent during a court hearing in Paris on Thursday morning.
The 26-year-old refused to attend a similar hearing in July.
News Source SkyNews