The Peugeot 607 was found on Wednesday with its hazard warning lights flashing and without number plates, police said.
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In the Thursday night operation in Boissy-Saint-Antoine, one of the women attacked police, and one suspect and one police officer were injured, Interior Minister Bernard Cazeneuve told reporters.
Several gas cylinders and documents in Arabic were found in an unmarked vehicle next the famous Parisian cathedral on Sunday.
Officials believe this might have been a test run for a terrorist attack, although there was no detonator present in the vehicle.
The first couple, who were detained at a service station on a road in southern France, were known to the security services for having links to radical Islamists.
French police arrested the second pair on Wednesday evening and were taken into custody, a judicial official said on Thursday. Her father, who is also understood to be the owner of the auto, was detained briefly after attending a police station to report his daughter missing on Sunday.
The two men, who are brothers, and the two women were transferred to Paris to be questioned by investigators trained in counterterrorism.
Anti-terrorism units found that the documents of the auto were in Arabic language.
The auto owner was taken into custody earlier this week but later released.
The owner of recovered vehicle was briefly detained and later released but his “radicalised” daughter is being sought by police, the Paris prosecutor’s office said.
In November, 130 people died in Paris in a series of terror attacks carried out by so-called Islamic State (IS).
Her father has told officers that she was “radicalised as a teenager”, and had expressed the wish to go and fight with ISIS overseas.
France remains on maximum alert after calls for attacks on the country.
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Hollande’s speech followed a deadly summer in France in which 86 people were killed when a truck ploughed into a Bastille Day crowd in the southern resort of Nice.
