Singles wins for Martina Trevisan and Jasmine Paolini gave Italy an unassailable lead in their Group D clash in Seville.
Trevisan recovered from a slow start to beat the experienced Alize Cornet 2-6 6-2 6-2 in the opening rubber.
The 27-year-old Paolini then battled back from 4-2 down in the deciding set to beat Caroline Garcia 7-6 (8-6) 5-7 6-4 in a match lasting two hours and 39 minutes.
France did manage to get a consolation victory in the doubles as Garcia teamed up with Kristina Mladenovic to edge out Trevisan and Elisabetta Cocciaretto in a deciding tiebreak.
Italy have now beaten France five times in their last seven meetings in the flagship women's team competition.
"Tomorrow will be another day and will be very tough day, for sure," Italy captain Tathiana Garbin told reporters.
"I think right now everything is still open."
Italy face Germany on Thursday.
The home fans inside the Estadio de la Cartuja were hoping to cheer on Spain to victory against Canada, but things did not go to plan.
Canada's world No.319 Marina Stakusic was far too good for 65th-ranked Rebeka Masarova in a 6-3 6-1 victory.
Former US Open runner-up Leylah Fernandez then beat Sara Sorribes Tormo 7-6 (10-8) 7-6 (9-7) in a scrap of almost three hours.
Thursday's action will also see reigning champions Switzerland attempt to stay alive in Group A as they take on the United States.
Australia will also be looking for their first win when they take on Kazakhstan.