The couple, aged 27 and 26, were placed in custody late on Wednesday, Xinhua news agency reported citing BFMTV.
The arrests follow the detention of the 34-year-old owner of the abandoned car and a 29-year-old woman, who were both later released.
The car owner is on the intelligence services watch list for radicalisation.
The car, a Peugeot 607, had no registration plate and its hazard lights were flashing when it was found near the Notre-Dame Cathedral. The vehicle contained seven gas cylinders, including an empty one, on the front passenger seat, in addition to three diesel cans. However, no detonators were found.
Anti-terrorism units found that the documents of the car were in Arabic language.
France has been on high alert since November 13, last year, when at least 130 people were killed in Paris in terror attacks. In July, this year, the country saw two more terror attacks -- one in Nice in southern France which claimed 86 lives and the other in a church in northern France.
