If this year's Roland Garros was wide open, then Wimbledon could be the same, and Williams believes she can be the one to take advantage.
Mladenovic will have French company in the quarter-finals, with either Caroline Garcia or Alize Cornet to join her after their round of 16 match.
Fourth-seed Rafa Nadal continued his ominous march towards a potential 10th French Open title by beating compatriot Roberto Bautista Agut 6-1 6-2 6-2 to reach the last eight.
But Mladenovic said the crowd was largely balanced, aside from at one stage screaming between Muguruza's first and second serves.
But ultimately the rest of her game made up for it, although there must be a concern that she has expended too much emotional energy to go all the way. I made about 35 double faults.
"I was really looking forward to the French Open", Murray said.
Muguruza, 23, left her media conference briefly because she was so upset, before returning to reveal she was glad to relieve the pressure of being French Open champion. "I just give her credit for playing well every point, even in the first set". "But I will try". I believed a lot in my possibilities in the last match.
"Yeah, I expected a very tough match".
"It's not ideal, there are little problems but I fight as I can. I'd rather not say anything more".
The last repeat women's champion at Roland Garros remains Justine Henin, who won the tournament three consecutive years from 2005-07.
The World No. 5 spoke following the match of being treated unfairly by crowds as well as unsportsmanlike behaviour by her rival Mladenovic, saying "The crowd was really tough today".
The 11th-seeded Wozniacki had 15 fewer unforced errors than No. 8 Kuznetsova. However, Mladenovic has had the most impressive victories, which is more encouraging, while besides her win over Venus, Bacsinszky has beaten up on players ranked outside of the top-50.
"It's obviously very bad what's happening or what's happened the last few weeks and obviously what happened here (in Paris) in the past, as well", Wozniacki said. It's not, you know, because it's Timea that I must get my revenge. Honestly, no, I don't think it was unsportsmanlike or unfair or anything. At age 19, the 47th-ranked Ostapenko is also the youngest player in the tournament.
The second-seeded Karolina Pliskova and the No. 5 seed Elina Svitolina earned their delayed third-round victories due to Saturday's rain. And as Muguruza walked to the locker room after her defeat, she wagged a finger toward the stands before bursting into tears during her post-match interview.