Ashleigh Barty remains at the top of the rankings despite not having played since February due to the coronavirus pandemic.
The Ukrainian third seed is the highest-ranked player left in the tournament and could be on a collision course with Iga Swiatek, the conqueror of 2018 champion and title favourite Simona Halep.
French Open 2020: Petra Kvitova enters quarters after eight years; Sofia Kenin overcomes Fiona Ferro
Two-time Wimbledon champion Kvitova is through to the last eight at Roland Garros. Her best run in Paris came when she reached the semi-finals in 2012.
French Open 2020: Teenager Iga Swiatek ousts top-seed Simona Halep; Nadia Podoroska, Martina Trevisan in quarters
Swiatek, the only teenager who reached the fourth round, avenged a crushing defeat by Halep at the same stage last year. The Romanian won that match 6-1, 6-0, in just 45 minutes.
Unsurprisingly, Nadal has yet to drop a set in Paris against opponents with a combined ranking of 319, but the Spaniard knows tougher examinations await in his pursuit of Roger Federer's record 20 major titles.
Taking place four months later than usual due to the coronavirus, the early summer warmth normally associated with the tournament has been replaced by a bone-chilling 10 degrees.
French Open 2020: Scarves, winter coats all around on Day 1 as 'ridiculous' cold sparks player revolt
The French Open, which was pushed back from its traditional May-June slot due to the coronavirus, began in steady drizzle and temperatures struggling to reach 10 degrees (50F).
French Open 2020 will be daunting given little preparation, colder conditions and quick turnaround from US Open
An unusual season's final Grand Slam gets underway today at Roland Garros. There is little similar to previous French Open events with little preparation, quick turnaround, colder conditions, roof and floodlights on Parisian red dirt.
French Open 2020 Women's Singles preview: Favourable draw, spectacular form make Simona Halep firm favourite
Ahead of Roland Garros' return, Firstpost takes a look at the Women's Singles draw and attempts to determine the potential outcome of all four quarters
French Open 2020: Simona Halep says players need to thank 'everyone for fighting so hard' to make tournament possible
Delayed four months from its traditional spring billing, players must contend with vastly different conditions and far cooler temperatures than they are used to in the French capital.
Rafael Nadal's bid for a 13th Paris title, and a record-equalling 20th Slam, and Novak Djokovic's pursuit of a second triumph in the French capital, to take him to 18 majors, are vying with health concerns in the battle for public attention.
World number two Halep, 28, was competing in her third Rome WTA final, having finished runner-up in 2017 and 2018 on the clay at the Foro Italico.
Halep, who lost to Elina Svitolina in the 2017 and 2018 finals, will face either Karolína Plíšková or Markéta Vondroušová in Monday's championship match.
Italian Open 2020: Rafael Nadal crashes out after defeat to Diego Schwartzman; Novak Djokovic battles through to semi-finals
Eight-seeded Schwartzman meted out a punishing 6-2, 7-5 loss in Nadal's final warm-up before his bid for a 13th French Open, and record-equalling 20th Grand Slam in just over a week.
Italian Open 2020: Novak Djokovic loses his cool again weeks after US Open default; Simona Halep in semis
When Djokovic was broken at love to even the second set at 3-3, he slammed his racket to the red clay in anger. With the frame broken and the strings all mangled, Djokovic received a warning from the chair umpire.
Halep was ahead 6-2, 2-0 when Putintseva decided she was in too much pain to continue - having already taken an off-court medical timeout between sets.
Italian Open 2020: Novak Djokovic, Rafael Nadal enter quarter-final; Simona Halep, Karolina Pliskova also through to last eight
Nadal proved too strong for 25th-ranked Lajovic, who had valiantly but vainly launched a fightback after trailing 4-0 in the second set to the Spaniard.
Italian Open 2020: Simona Halep extends winning streak to 11 matches; Novak Djokovic beats Filip Krajinovic
Halep, who is actually on an 11-0 run overall stretching back to February, recovered an early break in the opening set and then overpowered her 29th-ranked opponent the rest of the way.
Italian Open 2020: Nadal makes winning return after over six-month layoff; Azarenka beats Venus in first round
Defending champion Rafael Nadal and Novak Djokovic made winning returns at the Italian Open on Wednesday with the top two men's seeds easing into the third round of the clay-court tournament in Rome.
The French Open which has been pushed back from May to a 27 September start, could host up to 11,500 spectators per day.