Australia got their Davis Cup finals campaign up and running at the second attempt as the Netherlands beat the tournament's record all-time winners the United States on Thursday.
Defending champions Canada swept aside Sweden to remain unbeaten and the Czech Republic made it two from two as well with a comfortable win over South Korea.
Australia, last year's runners-up, badly needed a result against France to retain any realistic hope of making the knockout final phase in Malaga next month after defeat to Great Britain in Manchester 24 hours earlier.
With only the first two from each of the four round-robin groups progressing a loss to the French who had swept aside Switzerland in their opener could have proved terminal for the Aussies' quest for a 29th title.
And they were up against it when Adrian Mannarino beat Max Purcell 7-6 (7/4), 6-4 to leave them under intense pressure in Manchester.
But world number 12 Alex de Minaur came good, defeating Ugo Humbert (FRA) 7-6 (7/2), 6-3 to level with Matthew Ebden and Max Purcell (AUS) beating Nicolas Mahut and Edouard Roger-Vasselin in the doubles to claim the all important Group B win.
"It feels like redemption from yesterday," said de Minaur, who had lost to Britain's Dan Evans the day before.
"I've normally delivered when I put on the green and gold so I'm happy I was able to reset from yesterday and deliver a must-win match," he added.
Australian captain Lleyton Hewitt reflected: "These boys have done the jersey proud yet again. For us to regroup and get the win against a quality team in France today was really important.
"It was backs against the wall, we dug deep and we're still hanging on."
France have a tough closing assignment against Great Britain not to mention a partisan sold-out 13,000 crowd on Sunday, with Australia facing the Swiss who take on the hosts on Friday.
Canada beat Sweden 3-0 in Bologna to remain undefeated in Group A after cruising past Italy in similar fashion on Wednesday.
They are seeking to become the first back-to-back champions in a decade.
This was a must win encounter for Sweden after their 3-0 loss to Chile on Tuesday.
Swiss legend Bjorn Borg's 20-year-old son Leo once again performed well in defeat on his Davis Cup debut, losing in three sets to Vasek Pospisil.
Gabriel Diallo had little trouble against Elias Ymer to clinch the tie with doubles duo Alexis Galarneau and Vasek Pospisil wrapping up a perfect day.
In Split the Dutch dished out a 2-1 defeat to the USA in Group D just as they had done at the same group final stage in Glasgow last year.
Botic Van de Zandschulp beat Tommy Paul 7-6 (7/2), 6-2 with Tallon Griekspoor following up with a tense three set win over US Open quarter-finalist Frances Tiafoe.
The Americans took the concluding doubles courtesy of US Open doubles champion Rajeev Ram and Austin Krajicek.
In Valencia the Czech Republic added to their opening Group C win over Spain to beat South Korea also 3-0.
All eyes on Friday will be on Novak Djokvoic, who enters the stage for Serbia against Spain fresh from his record-equalling 24th Grand Slam at the US Open.