Two French outsiders who have frustrated their admirers with their serial inconsistency, Alizé Cornet and Caroline Garcia, will meet in the fourth round of their home slam after wins of contrasting style on a day when rain ripped through the schedule at Roland Garros.

The unseeded Cornet’s was the bigger, quicker win – 6-2, 6-1 in an hour and 19 minutes over the world No10 Agnieszka Radwanska.

Garcia, the No28 seed, had a significantly lesser opponent in the world No109 Hsieh Su-wei – who was good enough to put out Johanna Konta in the first round and the talented American Taylor Townsend in the second – but struggled over two hours and 39 minutes before winning 6-4, 4-6, 9-7. That might be scant consolation for Konta, the world No8, who had expected to be here at least until the end of the first week.

The ever-smiling Cornet said later: “I was feeling just very happy. It’s a lot of emotion to qualify for the second week of your home slam – big relief, also, because I beat Aga just once in maybe nine matches that we played.”

This was, in fact, her second success against the elegant Pole in eight attempts, but she got the numbers that mattered right. As she told French reporters later: “Whether I play against a top 10 or top 100 opponent, anything can happen, so I don’t focus on numbers.”

Radwanska’s collapse was a major shock but she had no answer to Cornet’s fierce determination. “I enjoyed my time on court a lot, but I was very stressed before the match,” the French player said. “Even during the match, because I felt like I could beat her. When you have this feeling, you have to be focused from the first to the last point. That’s what I did.”

She will be just as wired up for Monday’s match against Garcia. “The crowd is going to be excited to see Caro and me play, to see two French women playing for a place in the quarter-final. I think they will not [favour] one or the other, but we will try to give them a good show.”

Garcia said of her trial against the Taiwanese star: “So many games were very tight at the end. Even when I was down, I kept fighting, tried to be more aggressive. The last week for me was very difficult. It’s good sometimes when you have this period to learn about yourself, about your team, about the people around you.”

She will know plenty about Cornet, of course, and will start as the underdog given that she is No43 in the world – although this has been an unpredictable tournament from day one. Also, she won their only previous match: 7-5, 5-7, 6-3 on the clay of Marseille seven years ago.

“I don’t need to prove anything to anyone,” Garcia said. “I’ve played tennis a long time. I already have done well, but I want to do better, for sure.”

Garcia is a fiery individual and has bounced back with resolve from a suspension handed down by the French Tennis Federation last year, along with her doubles partner, Kristina Mladenovic, for what they considered was “unprofessionalism” at the Rio Olympics. Their ‘crime‘ was to contravene Olympic regulations by turning up for their match in outfits that did not match. They were favourites and lost.

Mladenovic, meanwhile, is already through to the next round, after her rousing comeback against the American Shelby Rogers on Friday, and plays the defending champion, Garbiñe Muguruza, on Sunday in what could be the match of the day.

Elsewhere in the weather-wrecked round on Saturday, Carla Suárez Navarro, the 21st seed, beat the Russian 14th seed Elena Vesnina 6-4, 6-4 without fuss, and the world No4, Simona Halep – who doubted before the tournament started if she would be fit enough to compete at all – beat 26th seed Daria Kasatkina, of Russia, 6-0, 7-5.