On the comeback trail after giving birth to her first child, Bencic put the Swiss on the board with a dominant 6-3 6-1 win over Chloe Paquet on Saturday at Ken Rosewall Arena.
France then levelled the tie when Ugo Humbert defeated Dominic Stricker, 6-3 7-5.
Stricker, guided by Bencic, found redemption after fighting off French pair Elizane Lechemia and Edouard Roger-Vasseli to win 6-1 7-6 (7-4) in the mixed doubles.
"(Stricker is) a little bit worse than the little one. At least, she cannot talk back," Bencic joked.
"It was a pleasure playing with Dominic. It's so easy when it's on his serve. I'm just chilling."
TEAM SWISS FOR THE W!— United Cup (@UnitedCupTennis) They defeat France 2-1 🇨🇠#UnitedCup pic.twitter.com/yRJ5aJmaxPDecember 28, 2024
Former world No.4 Bencic returned to competitive tennis in October after giving birth in April and is among six women competing at next month's Australian Open using protected rankings.
At Perth's RAC Arena, rising star Leylah Fernandez got Canada off to a flying start by defeating Croatia's Donna Vekic 6-4 6-3.
Fernandez's compatriot Felix Auger-Aliassime takes on Borna Coric in the men's singles before the duo play Vekic and Ivan Dodig in mixed doubles.
Australia kick off their campaign against Argentina in the late Sydney tie, with Olivia Gadecki first up against Nadia Podoroska before Alex de Minaur plays Tomas Etcheverry.