Seven Britons qualified for the French Open and only two male players remain in contention.
Jack Draper is one of them. The 23-year-old is the highest British seed in either singles draw after the world number five put together an impressive clay-court swing.
Draper reached the final of the Madrid Open, losing in three close sets to Ruud, and was beaten by eventual champion Alcaraz in the Rome quarter-finals.
He will face Alexander Bublik in the fourth round, while compatriot Cameron Norrie will meet 24-time major champion Novak Djokovic.
Norrie beat fast-rising Jacob Fearnley in an all-British contest in the third round on Saturday.
It is the first time since 1963 that two British men have reached the fourth round at the clay-court Grand Slam.
Katie Boulter, the highest-ranked British woman in the singles draw, and Sonay Kartal both lost second-round matches on Thursday.
Emma Raducanu’s run in Paris was also ended in round two with a straight-set defeat by Poland’s Swiatek on Wednesday.
Jodie Burrage was the only British player to lose in the first round, beaten by former world number seven Danielle Collins in straight sets on day two.