Only five women have successfully defended their titles at the French Open - Margaret Court, Chris Evert, Monica Seles, Steffi Graf and Justine Henin.
Mahut lost the only other main-draw singles match he played on the ATP Tour this year and revealed he was contemplating passing up a wildcard for his home grand slam due to a back injury.
Speaking to Eurosport, Clijsters said anyone could win the tournament but Halep must still be the favourite for many.
The 38-year-old Williams lost in the first round for the fourth time in the last seven years at the clay-court Grand Slam tournament.
Potapova hammered 28 winners past the flailing Kerber, who had been struggling with a right ankle injury in the build-up to the event.
She told the AP she was happy her clay season was over and she "can now look forward to playing on grass".
The Russian continued her momentum following a 6-4 opening set victory to take four games in a row into the second set.
Third seed Roger Federer was in control throughout his first round encounter against Italy's Lorenzo Sonego with a 6-2 6-4 6-4 win on his return to Roland Garros.
Three years ago Djokovic became the first man since Australian great Rod Laver in 1969 to hold all four Grand Slams simultaneously when he beat Andy Murray to win the French Open.
It was the tournament where Andre Agassi and Steffi Graf triumphed for the last time on the red clay of Paris.
"Proud of the way I turned things around mentally in such a short space of time and still with a lot of improvement to go".
"I feel like I'm playing good tennis, but is it enough against the absolute top guys when it really comes to the crunch?" Kyle Edmund likes clay and made the third round here a year ago but he has won just one match on the surface in 2019 and is on a five-match losing streak.
Roger Federer's 20 major titles are unparalleled in the men's game, as are his cumulative 310 weeks spent at the top of the rankings - 237 of which came in succession from February 2, 2004 until August 17, 2008. Provided the 32-year-old stays fit, which is far from guaranteed, it seems only Djokovic offers a realistic threat.
Named after the French Open women's champion in 1938 and 1939, the Court Simonne Mathieu was about half-empty for the start of the match but continually filled as Muguruza fought back from her unsteady start in a westerly breeze that shook leaves on the tall trees overlooking the arena.
The last two of those were against Dominic Thiem and Stefanos Tsitsipas, both of whom play with a one-handed backhand, just like Federer. "Instead of the tournament becoming easier, it was going to become more hard because of the pressure".