The Frenchman caused one of the biggest Africa Cup of Nations shocks when he guided the Chipolopolo (Copper Bullets) to the 2012 title.
Dismissed as outsiders ahead of the tournament in Gabon and Equatorial Guinea, Zambia defeated star-studded Ivory Coast on penalties after a goalless final.
Hailed as a national hero, Renard was unable to repeat the feat this year with Zambia making a meek first round exit in defence of the title.
“Herve Renard has been released from the job of Zambia national coach,” national football association FAZ said in a statement.
“He has been offered a wonderful opportunity at Sochaux — FAZ and Herve have consulted and it has been agreed not to stand in his way.
“It is a compliment for a coach working in Africa to be head-hunted by a European club. It makes us proud to take ownership of Herve’s rise.”
Renard had two spells as Zambia coach, taking them to the 2010 Cup of Nations quarter-finals before brief spells in charge of Angola and Algerian club USMA.
He faces a tough task at Sochaux, who crashed 4-1 to Bordeaux Sunday and are second last on the Ligue ! table after nine rounds with just one win.
Patrice Beaumelle, assistant to Renard, will prepare Zambia for a friendly against Brazil on October 15 in Chinese capital Beijing.