Seven Britons qualified for the French Open, with Jack Draper and Cameron Norrie going furthest before exits in the last 16.
British number one and fifth seed Draper was beaten by Alexander Bublik in four sets, while Norrie lost to 24-time major champion Djokovic.
Norrie had beaten fast-rising Jacob Fearnley in an all-British contest in the third round.
It was the first time since 1963 that two British men had 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 in the second round.
Emma Raducanu’s run in Paris was also ended in round two with a straight-set defeat by Poland’s Swiatek.
Jodie Burrage was the only British player to lose in the first round, beaten by former world number seven Danielle Collins in straight sets.