Play was stopped after three games on Court Suzanne-Lenglen, and the players were instructed to stay on court. However, they both were unhappy with temperatures in the low 50s and made it clear they would rather wait indoors.
"I'm down to play whatever," Azarenka said to an official while sitting under an umbrella on her chair. "You know I'm not complaining here, but this is getting a little bit ridiculous."
The official then asked whether she would be willing to wait for a few minutes, and the No. 10 seed was clear with what she wanted to do.
"No, I'm not waiting here a couple minutes because I'm cold. It's 8 degrees [Celsius]. I live in Florida, I'm used to hot weather."
She then walked over to Kovinic, and asked what she wanted to do.
"Do you want to wait on court?" she asked. "No? It's ridiculous. It's too cold. What's the point? Sitting here like ducks."
The two then left and play was suspended on the court.
They returned about 50 minutes later and Azarenka won the match 6-1, 6-2 and advanced to the second round.
"I think it's very tricky at the moment to have these conditions," she said after the match. "So definitely not going to sit here and complain, but sometimes I think there are smarter ways to handle situations."
Azarenka wasn't the only player to take issue with the elements Sunday.
"I think the first hour the conditions were a disaster because it was still raining, it was windy and it was really cold," said Italy's Andreas Seppi, who lost to American Sebastian Korda. "So I think it was not good to go on court to play the first hour at least. I think they should postpone the match at least for one hour.
"You're here in a Grand Slam and everything, and trying to do your best. It was just, I think, messed up to go on court."
"At the end [the rain] was starting again, but I wanted to finish the match so quickly," she said. "But yeah, conditions are very different. I think it's harder to win a point. You have to work for the point a lot more. Lower bounces. But, you know, it's for both of the players. Everyone has to adapt their way to win the match."
"You know, most years it's pretty cold and rainy here, whether it's in May or right now," she said. "Obviously it was very cold and rainy and the courts are playing much differently than usual. Those are the conditions right now for everyone, so it should be interesting."
The French Open was moved from its traditional spring dates because of the global coronavirus pandemic. Play got underway Sunday, and the tournament will run through Oct. 11. Rain is in the weather forecast for six of the next seven days in Paris.
"I think the players, especially me, I'm very happy that we were able to play today," he said. "I mean, I went to bed last night thinking it was going to be a long day, one of those where I never really got on the court. The weather cleared, albeit it was a bit nasty out there.
"Even in May you can have some cold, damp conditions. But it's never really been this cold and this damp and windy. It's just one of those things. All of us are happy to be playing right now, be playing a Grand Slam. I think the FFT, the French Open, have done an incredible job putting this event on. The players are happy to be here."