French Open: Novak Djokovic, Iga Swiatek through at Roland-Garros as No 2 seed Elena Rybakina and Fran Jones exit

Novak Djokovic progressed to the third round of the French Open after seeing off French world No 74 Valentin Royer 6-3 6-2 6-7 (7-9) 6-3 amid a feisty Roland-Garros atmosphere.

With the Frenchman battling back to take the third set via a tie-break, Djokovic started to react badly towards the crowd at Court Philippe-Chatrier.

Indeed, the 39-year-old put his finger to his lips in a shushing action at several points, and after victory struck a familiar pose of playing a violin with his tennis racket from the court. The Serb was also booed by the Paris crowd.

Djokovic will next face Brazil's exciting 19-year-old Joao Fonseca in the third round for a place in the last 16 in Paris. Fonseca fought back from two sets behind to beat 20-year-old Croatian Dino Prizmic 3-6 4-6 6-3 6-1 6-2.

• Latest French Open scores, results and upcoming matches
• French Open: Order of Play and first-round draw, results
• Download Sky Sports app for analysis, news and video
• Not got Sky? Get Sky Sports or stream with no contract

"I've played two matches and I feel like I've played for two weeks," Djokovic said.

"The crowd were involved fully and it wasn't easy for me. It was a very hot day. I hope I do not play another Frenchman here!"

During the contest, Djokovic was heard saying: "They don't have respect, no respect, no respect" after his serve got interrupted by a spectator.

Meanwhile, Russian 11th seed Andrey Rublev was ‌given a three-hour workout in the Paris heat in a 6-1 1-6 6-3 7-6 (7-5) victory over Argentina's Camilo Ugo Carabelli to move into the ‌third round.

Exciting 19-year-old Spaniard Rafael Jodar is also through after a 6-1 6-7 (5-7) 6-4 7-5 victory over Australian James Duckworth.

Erratic Swiatek progresses as No 2 seed Rybakina falls, Britain's Jones knocked out

World No 3 Iga Swiatek continued ‌her bid to rediscover her best form at the French Open, reaching the third round with a 6-2 ​6-3 victory over Czech Sara Bejlek in a match littered with unforced errors.

The ​four-time champion, who has lost only ‌twice at Roland-Garros since 2020, had far too much ​quality for her opponent but made 38 unforced errors, including a series of double faults.

"I was not happy with my first serve, I need to look at what happened, I wasn't feeling the rhythm of the ball quite well so I'll adjust that in practice," said Swiatek.

Swiatek will ​next face fellow Pole ⁠Magda Linette for a place in the last 16, after the latter knocked out 2017 champion Jelena Ostapenko 6-2 2-6 6-2.

Ukraine's Yuliia Starodubtseva held off a late Elena Rybakina ‌comeback to shock the second seed 3-6 6-1 7-6 (7-4) in the second round, after the Kazakh recovered from 3-0 down in the deciding set but fell short in a ‌tense super tie-break finish.

Britain's Fran Jones is out after her fightback proved in vain as she lost in the second round to 27th seed Marie Bouzkova.

Jones was hugely emotional after posting her first Grand Slam main-draw win against Beatriz Haddad Maia in the opening round on Sunday.

Like her friend Emma Raducanu, who played on the same court in her first-round defeat, Jones recovered from losing 10 of the first 11 games only to ultimately go down 6-0 7-6 (7-3).

The defeat means Katie Boulter, who takes on Anastasia Potapova in the second round on Thursday, is the last British singles player remaining.

Swiss 11th ​seed Belinda Bencic was the first woman to move ‌into the third round after she registered a 6-4 6-0 victory over American Caty McNally.

With a heatwave still a factor in Paris, seventh-seeded Elina Svitolina extended a run of solid form with a 6-0 6-4 victory over Kaitlin Quevedo.

Svitolina is on an eight-match winning streak after raising the Italian Open trophy.

Argentina's Solana Sierra claimed the biggest win of her career by beating ‌13th seed and former finalist Jasmine Paolini 3-6 6-4 6-3 to reach the third round. The 21-year-old will face Romanian 18th seed Sorana Cirstea.

Watch the ATP and WTA Tours, live on Sky Sports or stream with NOW and the Sky Sports app, giving Sky Sports customers access to over 50 per cent more live sport this year at no extra cost. Find out more here.