It took two-time major winners Mahut and Herbert just 1 hour 54 minutes to take revenge for a loss to the Italian duo in the 2015 Australian Open final.
Lucas Pouille, the world number 11, will have the chance to clinch a semi-final spot for France for the third time in four years when he faces Fognini in the first of Sunday's reverse singles.
“Pierre-Hugues and Nico played the perfect match,” said France captain Yannick Noah. “Now we are going to prepare Lucas to beat Fabio — we will give 150 percent for this match.”
The winner of the tie will face either Spain or Germany for a place in the final.
Croatia, the 2005 champions, are also one win away from the last-four after Ivan Dodig and Nikola Mektic defeated the Kazakh pair of Timur Khabibulin and Aleksandr Nedovyesov 6-7 (2/7), 6-4, 6-4, 6-2.
“We played together for the first time and that's why we needed some time to find our game,” said Dodig.
On Sunday, world number three and former US Open champion Marin Cilic can wrap up the tie when he faces Mikhail Kukushkin, the world 92 in the first of the reverse singles.
Kukushkin stunned world number 28 Borna Coric in Friday's singles.
In Nashville, the United States became the first country to punch their ticket to the Davis Cup semi-finals on Saturday following a doubles win by Jack Sock and Ryan Harrison.
The pair had to work for the victory on the hardcourts which gave the Americans an insurmountable 3-0 lead and a berth in the semis for the first time since 2012.
Sock and Harrison needed three hours to dispatch Belgian debutants Sander Gille and Joran Vliegen in four sets 5-7, 7-6 (7/1), 7-6 (7/3), 6-4 in front of a crowd of 5,000 at the Curb Event Center.
John Isner and Sam Querrey lifted the United States into a 2-0 lead over last year's runners-up Belgium on Friday.
Isner needed three hours and 14 minutes to dispose of world number 319 Joris de Loore 6-3, 6-7 (4/7), 7-6 (10/8), 6-4, while world number 14 Querrey beat 110th ranked Ruben Bemelmans 6-1, 7-6 (7/5), 7-5.