"He's had his ups and downs in the last three or four years but came back swinging and revitalised after a six-month layoff last year", said Djokovic.
It was revenge for France's defeat by Britain in 2015 when Andy Murray inspired his nation to the title.
World number two Djokovic shrugged off his recent elbow injury to give Serbia a winning start in their quarter-final in Belgrade with a 6-3, 6-4, 6-2 victory over 24th-ranked Albert Ramos Vinolas.
"I have lost matches in my career before, I'm going to lose more", said Edmund. They were awesome the whole week.
"The atmosphere was great", Pouille said, praising the home support at the Kindarena in Rouen.
Djokovic, 29, starred in 2010 when Serbia defeated France in the final in Belgrade for their only Davis Cup title.
The United States stayed alive in Brisbane when late substitute Jack Sock and Steve Johnson beat Sam Groth and John Peers 3-6, 6-3, 6-2, 2-6, 6-3.
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USA captain Jim Courier replaced scheduled doubles player Sam Querrey with Sock about an hour ahead of Saturday's match, despite Sock having lost his singles match to Jordan Thompson on Friday. "But today we were able to regroup and get a win".
After winning the Qatar Open in his first event of 2017, Djokovic has not gone beyond the quarter-finals in any of the tournaments he's played, including a shock second-round Australian Open exit at the hands of Denis Istomin. "Whether you've won 15 Grand Slams or none, playing in front of your country like this is incredible".
World No. 16 Nick Kyrgios is scheduled to face Sock in the fourth rubber, before a possible deciding contest between Jordan Thompson and John Isner.
Simone Bolelli and Andreas Seppi sent Italy's tie into Sunday, but needed a fifth-set tie-break to down Belgium's Ruben Bemelmans and Joris De Loore 4-6 6-3 6-4 3-6 7-6 (8-6). "All in all, I'm very pleased". "It was a very tough match".
France are unable to call on the services of their top two players, Jo-Wilfried Tsonga and Gael Monfils, although they do feature world number 17 Lucas Pouille in their line-up. For me, we deserved it.
"We have a chance even though Nadal is not here", Martinez told www.daviscup.com.
France can wrap up the tie on Saturday when Nicolas Mahut and Julien Benneteau face Jamie Murray and Dominic Inglot in the doubles.