The last time a woman repeated her title at Roland Garros was Justine Henin, who won the Grand Slam event for three consecutive years from 2005-07.
Mladenovic, who is into her second career grand slam quarter-final, said she also found it tough playing in front of her home crowd.
Australian veteran Stosur was beaten by a player 14 years her junior in Ostapenko, but had reason to feel unlucky after being hampered by a hand injury.
"I think she speaks like 25 languages, I heard, so..."More news: Drug haul case: Thane court declares Mamta Kulkarni, Vicky Goswami as absconders
"When I got injured, my only hope was that I would get a second chance so I can play some of my best tennis again", said Martic.
"Everything wasn't ideal. There were a few concerns", Mladenovic said, before joking: "I made about 35 double-faults today, but everything's OK!"
The 24-year-old got off to a flying start against Muguruza, who peppered the court with unforced errors as the Frenchwoman opened a 4-1 lead.
The women's singles tournament at the 2017 French Open has been a odd one.
Mladenovic is ow now face Timea Bacsinzky in the last eight after the Swiss came from a set down to beat Venus Williams of the United States, the 2002 French Open champion, 5-7, 6-2, 6-1. I understand. I just think that they. sometimes should be a little bit more respectful.More news: Ex-US Ally, Noriega, Dies At 83
"Svetlana's a great player, especially on clay so I knew it wouldn't be easy", said Wozniacki, a two-time US Open runner-up.
"I love this tournament no matter what happens". But with her 37th birthday to come later this month, and as she continues to live with Sjogren's syndrome, the auto-immune disease that causes chronic fatigue and muscle soreness, it is still about the bigger picture for Williams.
The last repeat women's champion at Roland Garros remains Justine Henin, who won the tournament three consecutive years from 2005-07.
"And I think it was bad, when they kind of screamed between her first and second serve, but that's because they thought it's a double fault because the first serve was a let or something".
On the men's side, Rafael Nadal and Novak Djokovic advanced, but history was made when Japan's Kei Nishikori beat South Korea's Hyeon Chung 7-5, 6-4, 6-7 (4), 0-6, 6-4 when their third-round match resumed after being suspended Saturday night. Halep has been very impressive in her fourth matches thus far at Roland Garros.More news: Nashville leaning heavily on defense corps against Penguins
First up on each of the tournament's two main courts on Tuesday's schedule are women's matches: No. 13 Kristina Mladenovic of France against No. 30 Timea Bacsinszky of Switzerland at Court Philippe Chatrier, and No. 11 Caroline Wozniacki of Denmark against unseeded 19-year-old Jelena Ostapenko of Latvia at Court Suzanne Lenglen.