Reports on the ground suggest the man is about 30 years old, though he is yet to be named.
He is said to have a history of domestic violence.
The local French government has called on residents in the area to stay indoors.
Franceinfo suggests the incident started on Saturday night, when the man is said to have shot his ex-girlfriend’s new partner.
The gunman’s ex and her children were not injured. The family are now in police protection, authorities said.
When police arrived, the man fired at officers before fleeing into nearby woods, according to reports.
There have been no police injuries or fatalities.
Le Lardin-Saint-Lazare Mayor Francine Bourra told BFM Television that the suspect had been released from prison and was wearing an electronic bracelet.
"I believe that unfortunately [the situation] can last a long time," Ms Bourra said, adding the man was: "not at all inclined to dialogue and not ready to surrender".
"The man went overnight to his ex-partner's home. A dispute took place there, which led to the intervention of gendarmes and that is when the suspect shot at them. He then fled to woods nearby," Frédéric Périssat - prefect of Dordogne - told BFM television.