Both went into their matches as heavy underdogs; Watson against 2009 champion Svetlana Kuznetsova and Yorkshire’s Edmund against 15th seed John Isner.
As well as her title, Kuznetsova has reached at least the quarter-finals on six other occasions at Roland Garros and is having a strong season.
Watson competed well in the second set but her serve was vulnerable throughout and she went down 6-1 6-3 in an hour and 12 minutes.
The British No 2 did not hold her serve for the first 48 minutes of the match, losing her first five service games.
Watson, the last British woman standing, has made the second round at Roland Garros in five of the last six years but has not been able to take the next step.
She said: “I thought my opponent played just a lot better than me today. She played really well. First set I thought she was pretty flawless.
“Second set I had a couple chances here and there to get even, get back in there. But she just played really well on the important points.
Watson has reunited with coach Diego Veronelli after splitting from him in December but the Argentinian has a young family and is only prepared to travel for between 10 and 15 weeks a year.
Over the next few weeks Watson will be accompanied by mum Michelle. The pair were together for the highlight of the 24-year-old’s season, when she won her third WTA Tour title in Monterrey in February.
Asked if she would consider bringing in another coach, Watson said: “Right now, I’ve been happy the way it is. My mum, we argue a lot, but she is really smart when it comes to tennis. She’s been with me my whole career. I never listen to her, but when it’s about tennis I do.”
Edmund had done very well to come through a physical contest with Georgian qualifier Nikoloz Basilashvili in the first round, but this was a big step up in class.
The 21-year-old showed that he could trouble the world’s best with a blistering performance in the first two sets against David Goffin in the Davis Cup final last November before fading.
But facing the power of Isner was a different matter and one break in each set proved enough for the American, who triumphed 6-4 6-4 6-4.
Edmund had his chances, notably when he got to 0-40 in the sixth game of the second set, but Isner dug himself out of the hole.