When it comes to picking the winner of the French Open, no one is talking about Stan Wawrinka.

That’s despite the fact that the Swiss won the title here two years ago and warmed up for this year’s event by taking the title in Geneva last weekend.

But Wawrinka, who has won a grand slam title in each of the past three years, is utterly unbothered by his relatively low profile.

“I don't mind,” said Wawrinka, who played well in his 6-4, 7-6, 7-5 win over Alexander Dolgopolov of Ukraine.

“For me, doesn't matter if we talk about me or not. I'm No.3 in the world. I won three grand slams the last three years.

“I know what my level is, I know what I can do. I'm focusing on what I have to do to stay as long as possible here, and the rest I really don't mind.”

Even without Roger Federer here, the Swiss whose prominence has overshadowed Wawrinka for much of his career, Wawrinka is considered fourth favourite behind Rafael Nadal, Novak Djokovic and Andy Murray.

But the 32-year-old is completely at home on clay, as he proved two years ago, and having won Geneva, arrived with form and confidence.

“Winning the title (in Geneva) for sure gave me a lot of confidence,” he said, with Italy’s Fabio Fognini his next opponent. “I think here I'm playing great tennis, so we'll see.

“It's only been two matches, so it's a long way to go if you want to stay here until the end. So that's what I'm focusing on, trying to do the right thing match after match, and we'll see what's going to happen.”

Seventh seed Marin Cilic, No.8 Kei Nishikori and No.15 Gael Monfils all won through to the third round.

On the women’s side, title favourite Simona Halep cruised past Tatjana Maria of Germany 6-4, 6-3 but Karolina Pliskova, Elena Svitolina and Agnieska Radwanska were all pushed to three sets.

Second seed Pliskova, a runner-up at the US Open last September, battled past Russian Ekaterina Alexandrova 6-2, 4-6, 6-3 while Svitolina, who has won four titles in 2017, came back to beat Tsvetana Pironkova of Bulgaria 3-6, 6-3, 6-2.

Radwanska, seeded ninth this year, battled back for a 6-7, 6-2, 6-3 win over Belgian qualifier Alison van Uytvanck while Eugenie Bouchard crashed out 6-3, 6-0 to Anastasija Sevastova of Latvia, the No.17 seed.