Interior ministry officials announced that officers from the Brigade Anti-Criminalité division were called to the burglary at a Darty store just after midnight on Wednesday morning.
The officer, named as Cédric Papatico, was deliberately knocked over by the suspects who were driving a 4x4 Porsche Cayenne.
The officer was thrown several metres by the impact and died of his injuries at around 1.30am.
The attack took place at a large shopping centre in the south west town of Saint-Alban-Leysse.
"Last night the Brigade Anti-Criminalité (BAC) of Chambéry was called to a burglary in a large shopping centre," said Pierre-Henri Brandet, an interior ministry spokesman.
"The suspects tried to escape and deliberately drove into the officers and, as a result, a 32-year-old policeman died as a result of his injuries."
Radio station RTL reported on Wednesday morning that the dead officer was a father of a six-year-old girl.
A Porsche Cayenne fitting the description of that used by the suspects was later found burnt out in a suburb of Lyon, around 100 kilometres from the shopping centre.
President Nicolas Sarkozy told radio station France Info on Wednesday that "everything would be done to catch the murderers."