In the first incident, an assistant photographer was seriously injured when a gunman broke into the leftist newspaper Liberation, while in the second, a gunman fired shots outside the headquarters of French bank Societe Generale then took a hostage as he fled, The Wall Street Journal reported.
"The newspaper is traumatized," Liberation publisher Nicolas Demorand said.
A bank spokeswoman said there were no injuries or casualties at the bank.
The hostage was released on the Champs, a police officer said.
A police helicopter was seen above the main Paris thoroughfare as officials work to identify and capture the man.
Police were acting on the premise that the attacks involve the same man, the police officer told the Journal. The officer said the same bullets were used in both incidents.
Also, witnesses said in both cases the shooter wore a dark coat, police said.
It was unclear what prompted the attacks or whether they were linked, the Journal said.
Police barricaded the street near the Liberation's offices. Police also were deployed to the headquarters of national papers, including Le Monde, Le Figaro and Les Echos, and of radio station Europe 1, a police official said.
Radio France Internationale said another incident Friday involved an armed man storming BFM-TV, Paris, threatening journalists but not firing a weapon.