Prosecutors said in one of the letters Abdelhakim Dekhar had denounced media manipulation and capitalism.
Abdelhakim Dekhar was arrested on Wednesday after a major manhunt.
According to the French authorities, he has been jailed before – in 1998, for his role in a string of previous Paris shootings.
After his release he lived in Britain for several years before returning to France in July, the authorities said.
After a two-day manhunt, Abdelhakim Dekhar was arrested on Wednesday evening in a stationary car in an underground car park following a tip-off from a member of the public.
One of Abdelhakim Dekhar’s letters was found beside him in the car, with details of his wishes for burial, Paris prosecutor Francois Molins told a press conference.
Another letter was reportedly given to officials by the man who housed him.
This man, according to Francois Molins, had been away from the building until recently, but on his return saw photos of the suspect in the Liberation shooting and recognized Abdelhakim Dekhar, who on confrontation confessed to being the man behind the attack.
Francois Molins said the second letter spoke of a “fascist plot” and accused the media of participating in the “manipulation of the masses”.
Police said that when Abdelhakim Dekhar was arrested, it appeared he had taken medication and did not seem very lucid.
Some media sources have suggested he may have attempted suicide.
Abdelhakim Dekhar is believed to have been the third man in the so-called Rey-Maupin affair, named after a young couple with links to anarchist groups who bungled an attempt to steal weapons from guards and then hijacked a taxi in 1994.
In the subsequent chase and shootout, three policemen and the taxi driver were killed, as well as Audry Maupin.
Aufry Maupin’s girlfriend, Florence Rey, was released from jail a few years ago.
Their story was compared to the controversial American film Natural Born Killers.
At his trial in 1998, Abdelhakim Dekhar protested his innocence, claiming he had been recruited by the Algerian secret service to infiltrate the French far-left.
Abdelhakim Dekhar was sentenced to four years in jail but released soon after the verdict, having already served his time in pre-trial detention.
In the wake of the two shooting incidents in Paris, hundreds of police were involved in a huge manhunt and security was stepped up at all media outlets.
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