On Friday an armed man broke into the Paris offices of the 24-hour BFMTV but fired no shots.
Police have now been stationed outside all the main media offices in Paris.
There has been no official confirmation that the same man is involved in all three incidents.
A police helicopter is now hovering above the Champs Elysees, tracking the man suspected of shooting the Liberation photographer, says the BBC’s Christian Fraser in Paris.
Police are encouraging people to stay inside.
say the hostage-taker told the motorist he was armed with grenades.
At 10:15 local time (09:15 GMT), a gunman entered the Paris offices of Liberation, near the Place de la Republique in the east of the city, and opened fire.
He fired two shots from a hunting rifle, injuring a photographer in the chest and arm, before escaping.
Eyewitnesses said he was aged about 40 and was wearing a cap and a raincoat. He did not say anything, Liberation reported.
Some two hours later, the bank Societe Generale confirmed that a man opened fire outside its headquarters in the western business district of La Defense. No-one was injured, the bank said.
Liberation’s deputy editor Fabrice Tassel said the victim – who was shot in the chest – was fighting for his life.
The man – who has not been named – was said to be a freelance assistant photographer who had just arrived at the newspaper office to work on a fashion photoshoot.
Police have sealed off the area around Liberation’s offices. Interior Minister Manuel Valls has visited the scene, along with Culture Minister Aurelie Filippetti and the Mayor of Paris Bertrand Delanoe.
French President Francois Hollande asked Mr Valls to mobilise every means to stop whoever was responsible for the attacks and to shed light on the circumstances.
Liberation said three spent cartridges of buckshot had been found, along with traces of buckshot in the ceiling.
“In a democracy, when someone enters a newspaper office with a gun, this is very, very serious, whatever the person’s mental state,” said Liberation’s publisher Nicolas Demorand.
Mr Demorand said he would hold a news conference at 17:00 GMT.
In the next few hours, investigators will compare CCTV images from the two attacks to see if there are any similarities, BFMTV said.
A journalist from Liberation told BFMTV that the two security guards at the entrance immediately ducked down behind their desks when the man drew his weapon and did not see him clearly.