One of the victims, a woman, was beheaded after a knife attack at a church in Nice.
In his message Pashinian said that Armenia condemns terrorism in all its forms and manifestations.
“It is more than obvious that extremism and fanaticism have no justification or moral excuse,” Pashinian said.
“The people of Armenia share the pain and anger of the fraternal people of France. We express our deep condolences and sympathy to victims’ families and friends,” he added.
The latest terrorist attack comes amid increased tensions between France and Turkey as well as other predominantly Muslim countries over the publication of the Prophet Muhammad cartoons in the French satirical magazine Charlie Hebdo.
About two weeks ago a French teacher was decapitated outside his school in a Parisian suburb by an attacker who wanted to punish him for showing pupils cartoons of the prophet in a civics lesson.
After that attack Macron and his government vowed a crackdown on Islamic extremism, stressing that freedom of speech is one of the highest values in France. This stance has drawn anger from the Muslim world where many leaders, including Turkey’s Erdogan, have accused Macron of Islamophobia.