The man, who was not immediately identified, was arrested late Monday and was being questioned in the provincial capital of Salta by the investigating judge in the case, Martin Perez, a court official said.
The suspect was linked to the .22 caliber murder weapon, "possibly in its purchase or sale," a source close to Perez later told AFP.
The French women's bodies were found Friday by hikers on a trail in an area overlooking the city.
A man who rents horses to tourists in the area where the bodies were found, 43-year-old Francisco Tejada, who had been arrested Monday was later released for lack of evidence.
The victims – Houria Moumni, 24, and Cassandre Bouvier, 29 – were "brilliant students" of Latin American studies at the Sorbonne, the university's president Marie-Christine Lemardeley said.
They were believed to have been killed sometime last week after going on a hike in the rocky trails that offer panoramic views of Salta, some 1,600 kilometres north of Buenos Aires.
The two women entered the San Lorenzo Gorge on July 15, according to a park registry, but were believed to have been killed sometime between last Tuesday, July 26, and Thursday.
Police investigators searched the San Lorenzo Gorge area on Tuesday looking for any clue linked to the murders, a source close to Perez said.
The area contains an ecological reserve of lush vegetation at 1,300 metres above sea level where hundreds of tourists arrive daily for horseback riding or hikes.
One of the women was shot in the head and apparently sexually abused. The other was shot in the back. Relatives of the two women arrived in Salta on Tuesday where they were met by French consul general Patrick Flot.
The newspaper Clarin quoted a judicial source as saying Moumni, who was shot in the back while trying to flee, may have survived for hours before bleeding to death.
"Before being shot, Moumni was beaten and defended herself when her attacker was about to rape her. In fighting with her killer, she succeeded in breaking loose and began to run, trying to rapidly climb a hillside toward the path," the source was quoted as saying.
The source said investigators found a .22 calibre bullet where the women's bodies were found, which he said appeared to rule out the possibility they were killed elsewhere and then brought to the park.
Argentine Foreign Minister Hector Timerman said his country was "appalled by the terrible crime," in a letter to his French counterpart Alain Juppe, adding authorities were "working hard on the case."
In Paris, French justice could open a preliminary investigation into the murders if their families give permission, an official said.
Tejada, the first suspect arrested, told AFP police used violence in an effort to force a confession. Sources said the investigating judge was looking into those allegations.
"They beat me all over my body in an effort to get me confess," he said. "I do not know why they tried to incriminate me. I have no weapons in my house."