Cameron Norrie is the only British player left in the French Open singles after Johanna Konta and Heather Watson lost their first-round matches.
Norrie reached the second round of the men's event by beating American Bjorn Fratangelo 7-5 7-6 (7-5) 6-2.
British women's number one Konta, seeded 19th, lost 7-6 (7-5) 6-2 to Romania's Sorana Cirstea.
Earlier, Watson also made a first-round exit with a straight-set defeat by Kazakhstan's Zarina Diyas.
Watson, yet to progress beyond the second round in Paris, lost 6-4 7-5 as she was unable to pick up her first tour-level win since the Australian Open in February.
In-form Norrie safely through
British number two Norrie will play South African Lloyd Harris or Italian 26th seed Lorenzo Sonego after seeing off qualifier Fratangelo.
Norrie could meet 13-time winner Rafael Nadal in the third round should he find a way past either Harris or Sonego.
The in-form 25-year-old boasts the third highest number of ATP match wins this year (after Stefanos Tsitsipas and Andrey Rublev) and ensured British presence in round two of the men's draw following Dan Evans' defeat by Serbia's Miomir Kecmanovic on day one.
Although he remains without a first ATP title following defeats in the final of the Lyon Open and Estoril Open earlier in May, world number 45 Norrie continued his momentum with a 24th victory in 2021.
Fratangelo made Norrie work hard for the first set, in which the players exchanged early breaks of serve before Norrie seized the first of two set points.
The Briton took control with a 4-1 lead in the second, but he was pegged back to 4-4 by a stubborn opponent before prevailing in a topsy-turvy tie-break.
The American refused to go quietly, breaking back at the start of the third and saving three match points before Norrie wrapped up victory with an ace.
Konta struggles to find consistency
Former world number four Konta followed Norrie on court six, hoping to bolster the British representation in a tournament where she reached the semi-finals in 2019.
Although she is still ranked inside the world's top 20, Konta has only won three matches this year after limiting her time on the tour.
That has been down to a combination of a long-standing knee injury and concerns over travelling during the pandemic, but meant she did not look quite at the level required to test Cirstea.
The 31-year-old Romanian reached the final in Strasbourg last week and the recent contrasting fortunes of the pair became more evident as the match went on.
An evenly matched first set swung away from Konta when she missed a short forehand at 3-3 in the tie-break.
The Briton clipped the top of the net and watched the ball loop back towards her side of the court, while seeing the momentum of the match shift in favour of her opponent.
Once Cirstea took her third set point for the opener, there was little sign of a Konta comeback. She lost serve in the opening game of the second set, with more errors starting to appear as Cirstea upped her level.
The Romanian pinched Konta's serve again for a 4-1 lead, going on to serve out for a straightforward win that leaves Konta set to drop out of the world's top 30 after the tournament, meaning she may not be seeded for next month's Wimbledon.
'Watson has not brought her best this year'
Diyas, ranked 93rd in the world, will face Belgian 14th seed Elise Mertens following her victory against an inconsistent Watson.
Watson, 29, made the perfect start as she broke Diyas' serve in the opening game but the Kazakh, 27, closed out the first set with consecutive breaks as the Briton suffered an alarming dip, losing 15 consecutive points.
Beaten in the qualifiers at the Italian Open and Madrid Open in recent weeks, Watson saved five break points early in the second set before finding a break of her own.
Despite another gritty hold at 4-2, it was a similar tale for Watson as Diyas broke back to level at 4-4 - and once again in the 12th game of the set to seal victory.
Speaking on BBC Radio 5 Live Sports Extra, former British number one Laura Robson said: "The scream of frustration from Heather at the end of the match said it all. We all know she can play better than that and she has not brought her best tennis this year. It is a real shame.
"She is a great competitor and great mover but it has not been the Heather we know this year. Diyas played well and solid but didn't need to be as consistent because Heather gave her a few easy balls."