Abdelhakim Dekhar also was linked to the crimes by DNA, officials said. A letter found in the car where he was arrested made a reference to his own death, and a second letter found in the home where he had stayed the night before the shootings was delusional, the report said.
Dekhar, 48, is a former far-left militant, The Local.fr said.
France 24 reported the Paris prosecutor said Dekhar was now well enough to be questioned and is being investigated on charges of attempted murder and kidnapping. A police source confirmed to France 24 that a letter had been found in his car. The letter was "rambling" and showed a "clear lack of mental coherence," the source said.
Meanwhile, French President Francois Hollande praised police for their work tracking and capturing the suspect in attacks on two media facilities and a bank in Paris.
Authorities said the suspect Dekhar, arrested Wednesday, was imprisoned for four years for his role in a bank robbery that morphed into a killing spree in the 1990s, Radio France Internationale reported Thursday.
Hollande praised the "efficacy of the police and the justice system," saying Thursday authorities prevented the incident from becoming more tragic.
"All the facts indicate his involvement," Interior Minister Manuel Valls said of the suspect arrested in an underground parking lot in a town northwest of Paris.
Police tracked Dekhar after a friend with whom Dekhar was staying recognized photographs distributed by police and alerted authorities Dekhar told him that he had done "something stupid," RFI said.
Police found him semi-conscious in a vehicle in an underground parking lot in Bois-Colombes, a western suburb in Paris.
"Everything seems to show that he tried to commit suicide," Valls said.
Police said security videos and DNA tests indicate they have the person who has eluded capture since Friday, when he attacked the headquarters of BFM-TV, shot and seriously wounded an assistant photographer at the left-wing newspaper Liberation, and fired shots outside the headquarters of the Societe Generale bank.
The BBC reported Dekhar is a former officer in the Algerian army.