Serena Williams gave an ominous warning with a comeback victory against Ashleigh Barty, while Simona Halep cut a relaxed figure after dominating Taylor Townsend at the French Open.

Former world number one Williams is playing a first major tournament since winning the 2017 Australian Open, after giving birth to her first child in September.

The America great was staring down the barrel of defeat after losing the first set to the 17th seed, but roared back for a 3-6 6-3 6-4 triumph.

Halep's progression was much more comfortable, a 6-3 6-1 victory over Townsend bringing up a 30th match win of the year, while Garbine Muguruza, Maria Sharapova and Angelique Kerber were all round-two winners.

SERENA PREVENTS BARTY PARTY

Barty had spoken of seeing facing Williams as an opportunity, and it was one the Australian looked like grasping.

However, the 23-time grand slam victor turned the match on its head and, as she started dominating the rallies, a fourth French Open title appeared a realistic possibility.

HAPPY HALEP FEELING RELAXED

Halep is one of the most talented players on the WTA Tour without a grand slam, having lost the French Open final twice and this year's showpiece at the Australian Open.

The world number one has openly admitted to struggling to cope with pressure of big matches in the past, but says she is feeling more relaxed on court.

"I feel happier on court now to play matches, and also when I practice," she said.

"You know I also felt the pleasure in the past, but I couldn't show it, so now I relax myself. I improved a lot in my thinking. I'm more positive."

MUGURUZA ON THE MARCH

Muguruza, a champion in Paris two years ago, was up against home favourite Fiona Ferro on Court Suzanne Lenglen, but she coped with that pressure to secure a routine 6-4 6-3 win.

The two-time grand slam winner conceded she did not play her best, but says her focus is purely on racking up wins.

"I'm not thinking to show my best tennis. You know, all I want is to go out there, compete, and win," she said. "It doesn't matter if my shots are not for the picture. It's fine. I'm happy with fighting."

Kerber was a class above Ana Bogdan in a 6-2 6-3 win, while Sharapova saw off Donna Vekic 7-5 6-4 to set up a heavyweight clash with sixth seed Karolina Pliskova, who needed three sets to defeat fellow Czech Lucie Safarova.