• Dart fell to a 1-6 6-1 6-2 loss to France's Elsa Jacquemot, while Jones had to retire against Ylena In-Albon.
• It will be the first time no British woman has featured in the main draw at a Grand Slam since the 2009 US Open.
There will be no British women in the French Open main draw after Katie Boulter, Harriet Dart and Fran Jones exited in the second qualifying round.
British number three Boulter was beaten 6-2 2-6 7-6 (10-3) by American 19-year-old Ashlyn Krueger at Roland Garros.
Dart fell to a 1-6 6-1 6-2 loss to France's Elsa Jacquemot, while Jones had to retire against Ylena In-Albon.
It will be the first time no British woman has featured in the main draw at a Grand Slam since the 2009 US Open.
World number 316 Jones, who beat Coco Vandeweghe on Monday, was left in tears after the 22-year-old was forced to retire because of a shoulder injury when trailing 4-1 in the first set.
Fellow British women Heather Watson, Katie Swan and Lily Miyazaki were all beaten on Tuesday.
Emma Raducanu, who would have received a place in the main draw, is out of action following operations on both her wrists and an ankle.
In the men's qualifying at Roland Garros, British number five Liam Broady, Jan Choinski and Ryan Peniston all suffered defeats.
Broady lost 6-4 0-6 6-3 to American 21-year-old Emilio Nava.
Peniston went ahead against eighth seed Radu Albot but the Romanian came back to clinch a 2-6 6-2 6-4 win, while Choinski lost 3-6 6-4 6-0 to Austria's Sebastian Ofner.
Cameron Norrie, Dan Evans, Kyle Edmund and Jack Draper will be Britain's only representatives in Paris, after Andy Murray withdrew to prioritise the grass-court season.
The draw for the French Open takes place at 13:00 BST on Thursday 25 May.
In Lyon, Britain's defending champion Norrie began with a 6-3 6-4 victory over Belgium's David Goffin.
The British number one, seeded second after Canada's Felix Auger Aliassime, will play Argentine sixth seed Sebastian Baez in the last eight as he continues his French Open preparations.
"It's such a special tournament for me, winning my first clay 250 this time last year, and I really like this tournament," Norrie said.
"I feel really good here. It's good to be back and good to get a straight-set win today."
Britain draw home tie for Billie Jean King Cup play-offs
It was announced on Wednesday that Great Britain will play their Billie Jean King Cup play-off tie against Sweden at home in November.
The winners will earn the chance to qualify for the 2024 Finals, while the losers will be relegated to a regional competition.
Each play-off tie will consist of five matches, with two singles matches on the first day and two singles matches followed by a doubles match on the second day.
The draw for this year's Finals, which will be held in Seville, has thrown up a strong group involving defending champions Switzerland, the Czech Republic and the United States.