The suspect, a 48-year-old man known to authorities for child custody disputes, was “discovered dead” several hours after fleeing the home in an isolated hamlet near Saint-Just, a village south of the city of Clermont-Ferrand, Interior Minister Gerald Darmanin said in a tweet.
He gave no further details on how the man died.
“Our security forces put their lives at risk to protect us. These are our heroes,” President Emmanuel Macron said in a tweet.
The man opened fire at two officers who arrived at the house shortly after midnight after being alerted to a reported domestic assault.
One was killed immediately and the other shot in the thigh before the man set fire to the house, where a woman had climbed onto the roof.
Two further officers, responding to the scene, were then fired on and killed, according to the prosecutor’s office in Clermont-Ferrand.
Police reinforcements and firefighters were rushed to the scene, and all roads leading to the house were blocked off.
The woman was safely rescued, and was being questioned by police.
The victims were aged 21, 37 and 45, the interior ministry said.
Aside from terror attacks, shootings of police officers in France are relatively rare.
Last May, a man fired at police from his house in the Gironde region of southwest France, wounding one officer. As he was about to fire again, he was shot dead by police.