A second person was seriously injured in the attack in the southern suburb of Montrouge, after which the gunman fled.
It is unclear of the incident is related to the Charlie Hebdo massacre.
Police have made seven arrests in the hunt for two brothers, Cherif and Said Kouachi, the main suspects in Charlie Hebdo massacre. A third has surrendered.
Arrest warrants were issued for Cherif and Said Kouachi, said to be “armed and dangerous”.
Sources close to the investigation told AFP news agency of a report that the two had been spotted on January 8 in a car on a road in the Aisne region of northern France.
They were reportedly recognized by the manager of a service station near the town of Villers-Cotteret, and still armed.
A minute’s silence was observed at midday across the country as France observed national mourning for the victims of the Charlie Hebdo attack. The bells of Notre Dame Cathedral in Paris tolled in mourning.
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