That's it for our live text and radio coverage of the French Open today.

You can find details of today's action from Roland Garros on the BBC's tennis page and we'll be back again tomorrow with more second-round action, so hope you can join us then!

Jannik Sinner continues his bid for a career Grand Slam tomorrow - he's first on Court Philippe-Chatrier against Juan Manuel Cerundolo, who defeated Great Britain's Jacob Fearnley in round one.

Aryna Sabalenka, Naomi Osaka, Amanda Anisimova and defending women's champion Coco Gauff all play their second-round matches.

And Katie Boulter, the sole remaining British player in the singles draws, takes on 28th seed Anastasia Potapova.

Image source, Getty Images

Earlier today, Ukraine's Yuliia Starodubtseva caused the biggest shock of the tournament so far as she defeated world number two Elena Rybakina - here's what she had to say in her on-court interview:

"I'm super happy, Elena is one of the top players, she's had an incredible year and I'm super proud of myself that I was able to do this today. It was a hard third set but I got it done."

On coming back from a set down: "I feel someone like Elena, I expected it from her. You can't be thinking that it's going to be easy today. Even at 3-0 [ahead in the third set] I had a feeling that it might not be that easy which it appeared not to be. Tough match but happy to be the winner today."

On playing well at the French Open: "I think clay is not the worst surface for me and the crowd was very, very nice to me today - I really felt the support today and I heard my name quite a few times and I really appreciated it."

Greg Rusedski
Former British number one on BBC Radio 5 Live

On whether Novak Djokovic is Jannik Sinner's biggest threat at the French Open:

Alexander Zverev hasn't come close but I still think it's him; even though he hasn't done well against him [before].

Novak - I need to see a little bit more. After the third round, if he comes through that's a huge statement so let's wait until after the third round. I don't see him yet as the biggest rival but could he become so? Yes, if he wins the third round.

Image source, Getty Images

Novak Djokovic, who beat France's Valentin Royer in a gruelling match lasting almost three and three-quarter hours, spoke in French in his post-match interview: "Obviously the feelings on the court are different when you win. It was a tough match in very difficult conditions."

For the second match in a row, Djokovic was taken to four sets by a Frenchman: "I think Valentin [Royer] deserves a big round of applause for his performance today. I hope I won't play any more French players for the rest of the tournament!"

Greg Rusedski
Former British number one on BBC Radio 5 Live

At one stage, Novak's second serve was averaging about 75-85 mph and against a big returner you're going to get punished with that.

Physically, he looked like he'd been struggling. A lot of the players have been struggling with this heat but the good news for Djokovic is he's going to start playing in the evening and, like Novak does, he finds solutions.

Even at 39 years of age, it's just impressive and I have nothing but respect for him.

Image source, Getty Images

• Second seed and Australian Open champion Elena Rybakina is out of the French Open - Rybakina won the opening set but was beaten in a deciding-set tie-break by Yuliia Starodubtseva.
• Britain's Francesca Jones was also knocked out in the second round by Czech 27th seed Marie Bouzkova. Jones twice had the chance to serve out the second set to level the match, but eventually lost 6-0 7-6 (7-3).
• Iga Swiatek and Elina Svitolina made it safely through to round three in straight sets.
• Novak Djokovic was made to work hard for his second-round victory against Valentin Royer, eventually winning in four sets.
• Andrey Rublev and Jakub Mensik are among the players also through to the third round of the men's singles - Mensik required treatment on court after completing victory over Mariano Navone 13-11 in a deciding-set tie-break. That match lasted four hours and 41 minutes.

Greg Rusedski
Former British number one on BBC Radio 5 Live

Impressive stuff from Novak. He battled.

His second serve points weren't great today but it's all about finding a way to win. I don't think you saw his dancing celebration because I don't think he had much left with his legs to dance with.

He's 39 years of age and is breathing quite hard at the end of this match. This was a true test for Novak. He's going to have to up his level again if he's going to continue in these championships.

Image source, Getty Images

Just as he has all match so far, Valentin Royer refuses to back down, and holds serve in gritty fashion.

So, getting on for an hour after he had a match point in the third-set tie-break, Novak Djokovic will be serving for the match.

Novak Djokovic pumps his fist as he holds to move within one game of victory.

It's a tired-looking return from Valentin Royer on the final point - but he will need to summon up some more energy as now he will be serving to stay in the match.

After losing his previous service game, Valentin Royer holds to love.

Novak Djokovic doesn't bother to chase down the ball on one point and also seems to be stretching out his limbs. Is he trying to conserve energy to haul himself over the finish line?

Image source, Getty Images

Greg Rusedski
Former British number one on BBC Radio 5 Live

We're getting our answer after that third set where we asked which Novak was going to turn up and he's looking like that young 39-year-old.

This is impressive - never discount a great champion.

Novak Djokovic has got the bit between his teeth, yelling and pumping his arms up and down after a forehand winner.

Court Philippe-Chatrier is covered in shadows now and Djokovic has discarded his cap.

So far in this set, he is managing to keep his cool, and he holds to edge nearer to the finish line.

Greg Rusedski
Former British number one on BBC Radio 5 Live

Just a brilliant point there from Djokovic. He pushed Royer so far back to get the break and Novak looks like he is going to up his level.

Novak Djokovic appears to have settled down emotionally after the frustration of missing out on the third set.

Valentin Royer is still going for broke but Djokovic has buckled down and manages to make the breakthrough by working his opponent around the court before delivering a killer forehand winner.

Image source, Getty Images

Even when Novak Djokovic looks weary, he can still pull off the most incredible shots.

On the run, he manages to squeeze a forehand winner around the net post - Valentin Royer can only smile in amazement.

Even Djokovic, who has been out of sorts this afternoon, smiles bashfully - maybe that can give him a bit more energy against an opponent who is 15 years younger.

Greg Rusedski
Former British number one on BBC Radio 5 Live

For Novak, it's finding a solution and trying to get this done in four sets and then getting better if he finds a way to win the match.

If this goes the distance it will be very disconcerting for Djokovic because I can't remember the last time he was up a break on two occasions while up two sets for love and was pushed into a tie-breaker.

Image source, Getty Images

Valentin Royer is continuing to take the match to Novak Djokovic, and is refusing to take a step back, rushing forward to attack whenever he can.

It's another love service game from the Frenchman.

Before the start of the fourth set, Novak Djokovic is in discussion with umpire James Keothavong.

It seems like he's not happy with the shadows that are now falling over Court Philippe-Chatrier but the 39-year-old will know that he should have been back in the locker room by now.

Djokovic finally holds serve in the first game of the fourth set - but it takes him almost 10 minutes to do so, which won't improve his mood.

He's been on court almost three hours now, which was definitely not part of the game-plan.