Djokovic is last on Court Philippe Chatrier, against No. 19 Albert Ramos-Vinolas of Spain, while the fifth-seeded Muguruza plays No. 13 Kristina Mladenovic of France on Court Suzanne Lenglen after Rafael Nadal plays Spanish compatriot Roberto Bautista Agut.
"The crowd today was a little bit tough on me, but I understand. I understand. I just think that they were a little bit, sometimes should be a little bit more respectful", the 2016 champion told the gathered journalists.
This had the makings of another sweep for the Swiss, who led 5-1 in the first set, only for Williams to pound her way back with six straight games to take the set, 7-5, after an hour's battle.
Muguruza broke down in tears during her press conference and had to leave the room for a couple of minutes before returning. "It's all behind me now, so whatever happens in this tournament is not necessarily my concern anymore".
Asked whether she could hear Mladenovic yelling "forza" (come on) on her unforced errors, Muguruza replied: "No, I think she speaks like 25 languages, I heard".
The 24-year-old Mladenovic never had been past the third round at her home major - and has never made it beyond the quarterfinals at any other. She also was the runner-up to Williams at Wimbledon in 2015.But the Spaniard has been repeatedly answering questions recently about whether expectations are different now that she is a major champion and whether that sort of pressure might affect her on court.
Mladenovic will face Bacsinszky next, and Wozniacki meets Ostapenko.
Garbine Muguruza did not take kindly to the way spectators pulled for her opponent - her French opponent, mind you - at the French Open.
Meanwhile, No. 1 Caroline Wozniacki returned to the quarterfinals for the first time since 2010, eliminating 2009 champion Svetlana Kuznetsova 6-1, 4-6, 6-2. No. 20 Pablo Carreno Busta, and Djokovic vs. "I mean, I love playing here". The last woman representing France to win the country's Grand Slam tournament was Mary Pierce in 2000. In the victory, Mladenovic won 70 percent of her first serve points and 43 percent of her second serve points.
Bacsinszky is obviously the more experience player in these type of matches and has had to work less to get to this point.
An oldie but goldie French champion, Francesca Schiavone, drew the defending champion in her opener: It was no contest.
With Alize Cornet taking on Caroline Garcia in the fourth round on Monday, two Frenchwomen will be in the last eight for the first time since 1994.