Fabio Fognini and Matteo Berrettini won their singles matches over Benoit Paire and Gael Monfils respectively to take an unassailable 2-0 lead in the Group B tie before Nicolas Mahut and Vasselin combined for a consolation point from the doubles.
“It's a great team, great guys,” said Berrettini. “We are enjoying on court, but off court as well. I think when you're playing for your country, for your team, it's something special.”
Italy, who won their opening tie against Austria on Tuesday, advance as group winners to the semi-final.
France will take on Austria for the runners-up spot from the group.
Showdown
In other matches in the 12-team event, Germany beat Canada 2-1 in Group A and will next face Serbia for a place in the semis.
In Group D, hosts Australia kept their hopes alive with a 2-1 victory over Greece.
Spain will advance to the last four though if they beat Greece on Thursday. World number two Rafael Nadal is expected to play in the match.
On Tuesday the 33-year-old withdrew from his game against Australia’s Alex de Minaur due to a back problem.
