Authorities had said earlier they were searching for the two daughters of the owner of the grey Peugeot 607 abandoned on Sunday near Notre Dame, which draws millions of visitors every year.
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Police sources said on Tuesday that no detonator device was found in the auto, but the presence of diesel-filled canisters added to concerns that there had been a plan to explode the vehicle.
Police were forced to shoot her, leaving her severely wounded.
All three were seized together in Boussy-Saint-Antoine, south of Paris, an inquiry source said. One of the women attacked police, and an intelligence officer was hospitalized with a knife wound to the shoulder.
Police arrested three women on Thursday evening, a police official told Reuters.
The suspects, respectively aged 19, 23 and 39, were “likely preparing violent and imminent attacks”, he added.
The auto had been abandoned in a no-parking zone with its hazard lights on, and without its registration plates.
The 19-year-old is the daughter of the owner of the abandoned vehicle, according to two officials who were not authorized to be publicly named discussing an ongoing operation.
Police investigators announced on Wednesday that a vehicle loaded with six gas canisters, five of which were full, had been discovered on Saturday night close to the Notre Dame Cathedral in Paris.
Although the cylinder on the back seat was empty, five full cylinders were discovered in the trunk of the auto, as were three bottles of diesel fuel. No detonator was found.
“If it was an attack plot, the method was very odd”, a police source said Thursday.
France is on alert after a string of attacks by militants linked to the “Islamic State” (IS) group and threats against key buildings.
France has been hit by a series of terror attacks claimed by the Islamic State.
In July, 86 people were killed when a truck ploughed into a Bastille Day crowd in the southern resort of Nice with IS saying it was driven by one of its followers.
Less than two weeks later, two young jihadists murdered a priest near the northern city of Rouen.
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France has been on high alert after a series of attacks in France in November previous year and July.
