Serbia, champion in 2010, is on the verge of advancing to the semi-finals after Viktor Troicki saw off Pablo Carreno Busta 6-3 6-4 6-3 in the second rubber.
With the elbow now healed, Djokovic said earlier this week at Davis Cup that he enjoyed the time off to spend with his wife and family.
Pouille gave hosts France a winning start in the quarter-final with a 7-5, 7-6 (8/6), 6-3 victory over Kyle Edmund.
Although Djokovic is still number two in the world the 29-year-old remains a shadow of the man whose maiden Roland Garros title in June last year allowed him to boast ownership of all four majors.
Australia is also firmly on course to advance from its tie with United States courtesy of wins from Jordan Thompson and Nick Kyrgios in Brisbane.
"We've got a big tie against USA".
The US head to Australia with world number 15 Jack Sock in their squad along with John Isner.
On a ideal day for all four of the quarter-final hosts, Australia were 2-0 up on the United States in Brisbane, closing in on a semi-final date against Belgium who were 2-0 ahead of Italy in Charleroi.
"I'm still very emotional out there".
Belgium, runners-up in 2015 to Great Britain, are seeking their second semi-final appearance in three years, while the Italians are bidding for their first since 2014.