Herbert and Mahut, who have won two grand slam doubles titles together, lost only two points on serve in the first set and were barely troubled in a one-sided match on indoor clay at Pierre Mauroy stadium.
They did lose their focus in the third set after opening up a 5-2 lead, but played a near perfect tiebreak to seal the win on their first match point.
“I will never forget it. I had never experienced so many emotions in my career,” Mahut said.
Serbia took the first point in the tie when Dusan Lajovic beat Lucas Pouille in four sets before Jo-Wilfried Tsonga levelled it up by beating Laslo Djere in straight sets.
Tsonga is set to face Lajovic in a potentially decisive reverse singles on Sunday.
Belgium are hosting Australia in the other semi-final.
France are bidding to win the Davis Cup for the first time since 2001. They have reached three finals since, the most recent in 2014 against Switzerland.
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