Using interior ministry figures, the body counted 222 Islamophobic acts compared to 37 in the first quarter of 2014.
Most of these acts, 178, were recorded in January after three Islamic extremists went on a three-day killing spree in and around Paris that left 17 people dead.
Abdallah Zekri, president of the observatory, said the recent rise in Islamophobia was unprecedented since the body was set up in 2011.
The acts include violence against men and women, some of whom were pregnant, vandalism and destruction of Muslim places of worship or businesses and "Nazi" graffiti on mosques.
"It is the first time we have recorded grenades being thrown or guns fired," Zekri said.
He said the attacks on the Charlie Hebdo magazine, a Jewish supermarket and the shooting of a policewoman between January 7-9 "in no way justify this peak in hatred or vengeance against French Muslims who are not responsible for or guilty of terrorist acts."