Jankovic and Venus Williams were the leading players to progress in the women’s draw on day two, which was cut short when the heavens opened midway through the afternoon.
While Williams, the eighth seed, needed three sets to get past Tzipora Obziler just before the rain came down, Serbia’s Jankovic was a 7-6 (7/3) 6-2 winner over Monica Niculescu in the same half of the draw.
The likes of second seed Ana Ivanovic and 2002 winner Serena Williams progressed on Sunday, but Jankovic does not believe she should be hoisted up into that company as the challenge hots up to succeed retired reigning champion Justine Henin.
“I don’t really look at myself as a favourite,” said the 23-year-old, who reached the semi-final here last year before losing to Ivanovic. “There are other girls that are favourites.
“But I’ve been playing well the last few weeks on clay and I’m learning to construct the points. Justine was the one I had most trouble with. I could never beat her – now that she’s gone, I’ve more of a chance.”
Jankovic came to Paris on the back of a tournament win in Rome last week but she struggled to find her best form against Niculescu.
“I got quite confused because I did not know her game and I didn’t know what to expect from her,” added Jankovic. “I didn’t play well tactically, I didn’t do what I was supposed to do.”
Williams had major problems against her veteran Israeli opponent, who battled gamely before slipping to a 6-3 4-6 6-2 defeat on the Philippe Chatrier court.
After a convincing start, things started to go awry for Williams towards the end of the second set and she then fell behind early in the third as light rain started to fall.
Obziler, 35 and a relative unknown, faded as the set wore on and her American opponent finally took advantage.
“Sometimes a tennis match isn’t always won as quickly as you want,” Williams said.
“She made some good shots and fought really hard. It was strange with the rain coming and going – it was important to concentrate. Thankfully I got through it before it started.”
Only one seed – Alona Bondarenko (23) – fell yesterday, with Petra Cetkovska of the Czech Republic taking the scalp of the Ukrainian.
Play was abandoned for the day at around 7pm local time, with the likes of sixth seed Anna Chakvetadze and home favourite Amelie Mauresmo still to get on court.
Meanwhile in the Mens section, Guillermo Coria’s French Open campaign came a swift end yesterday, but the injury-prone Argentinian left Roland Garros insisting: “I’m back.”
Coria, the runner-up here in 2004 when he lost to compatriot Gaston Gaudio in five sets in the final, has seen the last two years of his career ruined by shoulder and back injuries.
But in his first grand-slam event since the 2006 US Open, Coria was impressive and despite his 5-7 6-4 6-1 6-4 defeat to 12th seed Tommy Robredo, his display on Philippe Chatrier court hinted at better things to come.
Once on the verge of retirement, the 29-year-old now has fresh hope for the future.
“One month ago, I didn’t think I would be here at Roland Garros, and you know what that would have meant to me,” he said.
“But I took up the challenge and I can tell you the situation has changed.
“I feel great and I hope one day I will win the tournament.”
Meanwhile Roger Federer eased into the second round of the French Open with a 6-4 6-4 6-3 victory over American Sam Querrey.
It was a bad day for Richard Gasquet, as the eighth seed, was forced to pull out of the tournament yesterday because of a left knee injury. Cyprus’ Marcos Baghdatis was the highest seed to fall yesterday after he was thrashed by Simone Bolelli 6-2 6-4 6-2.