Investigators said the letters were "confused" and sought to explain his actions. In a press conference, Paris prosecutor Molins said the letters spoke of a "fascist plot," touched on "how suburbs are run" and accused the media of participating in the "manipulation of the masses".
One letter was incoherent and mentioned Libya, Syria and the situation in the Arab world, news channel BFMTV said.
The shooter opened fire with a 12-gauge shotgun at the offices of Liberation early on Monday, hitting a 23-year-old photographer's assistant as he hauled gear in the lobby, then firing another blast that hit the roof before leaving within seconds.
He then crossed the city to the La Defense business district on its western edge, where he fired several shots outside the main office of the Societe Generale bank, hitting no one.
He hijacked a car and forced the driver to drop him off near the Champs Elysees in the centre of the French capital, before disappearing.
Police say he was the same man who last Friday stormed into the Paris headquarters of a 24-hour TV news channel, BFMTV, briefly threatening staff with a gun before hurrying out.
Dekhar was suspected of being the third man in the so-called Rey-Maupin affair in 1994, which shocked France.
Investigators at the time compared the young couple to the infamous American outlaws Bonnie and Clyde.
Witnesses at the trial in 1998 described him as a mentor to the couple and accused him of exploiting their youth to manipulate them.
He argued that he had been a secret agent in the pay of Algerian security services, charged with infiltrating the radical left in France in search of those acting in coordination with Islamists in Algeria.
In the early 1990s Dekhar was known to hang out at squats used by left-wing radicals and which were often under police surveillance.
Maupin died of injuries sustained during a shootout with police and Rey, a middle-class student hitherto unknown to the police, was tried and sentenced to 20 years in jail. She was released in 2009.
Dekhar was acquitted of armed assault but found guilty of procuring the weapon and sentenced to four years. He was released soon afterwards, having already served his time in pre-trial detention.