Belinda Bencic has led Switzerland to a 2-1 win over France to kick off their United Cup campaign, while Canada beat Croatia 2-1.

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 the mixed doubles 6-1 7-6 (7-4).

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.

"I think my level is higher than I expected it to be because I didn't expect to be here yet," Bencic said.

"Definitely the whole comeback went much faster than I anticipated and expected. It's super great.

"I didn't rush things. I was super careful with starting again. I didn't really want to put a time pressure on my comeback. I just wanted to see how it goes every day.

"I feel good with every match. I think definitely it's the physical part that needs improvement."

At Perth's RAC Arena, rising star Leylah Fernandez got Canada off to a flying start against Croatia by defeating Donna Vekic 6-4 6-3.

Borna Coric levelled the tie in dramatic fashion, overcoming a disastrous first set on the way to beating world No.29 Felix Auger-Aliassime 0-6 6-4 6-4.

"I'm not sure (how I won)," said Coric, who lost the first eight games of the match.

"I came out and I was not feeling my serve. It's obviously very tough to play against him when I'm not feeling it.

"I just tried to stay positive with the crowd here and I knew I was going to have my chances.

"Then I started to play better. It was absolute chaos (in the third set) but in the end, I had a little bit of luck."

But it was Fernandez and Auger-Aliassime who came up trumps in the deciding mixed doubles, defeating Croatia's pairing of Ivan Dodig and Lucija Ciric Bagaric 6-3 6-4 to secure the tie.