Top-30 ranked pair Benoit Paire and Gael Monfils won their singles matches to ensure France opened their ATP Cup campaign with victory over Chile.
On day two of the inaugural tournament in Brisbane, Paire opened with a 6-7 (3-7) 6-3 6-3 win over Nicolas Jarry.
Monfils sealed the Group A win by beating Cristian Garin 6-3 7-5.
Japan, without Kei Nishikori, won all three matches against Uruguay in Group B in Perth, while Argentina beat Poland 2-1 in Group E in Sydney.
Novak Djokovic, Rafael Nadal and Dominic Thiem all play later on Saturday as Serbia, Spain and Austria start their campaigns against South Africa, Georgia and Croatia respectively.
The 24-nation event is spread across three Australian cities - Brisbane, Perth and Sydney - and features six groups of four teams, who each play three round-robin ties.
The six group winners, plus the best two runners-up, will progress to the quarter-finals.
Great Britain, who are without Andy Murray after he pulled out through injury, lost their opening tie against Bulgaria on Friday.
Jamie Murray and Joe Salisbury were beaten in a thrilling deciding doubles match which ended at 02:47 local time in Sydney.