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.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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