The incident took place near Jean Racine School in Teisseire district of the city in the morning.
The two deaths were later confirmed by Prosecutor Laurent Becuywe to le dauphine newspaper, Russia Today reported.
The first victim, a man, died at the scene, the second succumbed to his injuries later, police sources said, adding that a third man is seriously injured.
Police and ambulances have been deployed to the scene.
The shooting was not a terrorism-related incident.
Grenoble was the scene of a horrific beheading last year wherein an employee of a US-owned gas factory killed his boss and left the severed head on the gates.
France has been on high alert following the November 2015 terror attacks in Paris that left at least 130 people dead.