The world number one tackles Sweden's Mikael Ymer, ranked 80, seeking a 32nd win in 33 matches in 2020.
Serena Williams will next face Bulgarian wild-card entry Tsvetana Pironkova.
Kvitova, a two-time Wimbledon winner, advanced from the first round for the 10th time in 11 appearances at Roland Garros.
Top-seeded Halep won 10 straight games in beating Sara Sorribes Tormo 6-4, 6-0 to reach the second round of the French Open on Sunday and extend her winning streak to 15 match
The 31-year-old 10th seed eased past Danka Kovinic, the world number 74 from Montenegro, 6-1, 6-2.
When the French Open begins in Paris on Sunday, Indian presence will be absent in the singles category.
Serena Williams can never be discounted as she launches another bid for a record-equalling 24th Grand Slam singles crown, but Roland Garros is the American's least successful major.
The new limit, reduced from 5,000 per day, was first announced by Prime Minster Jean Castex on Thursday.
The heavier conditions could suit hardcourt players more and negate some of Nadal's lethal topspin, possibly aiding Thiem who has finished runner-up in Paris twice in succession.
Ankita's defeat means that no Indian will compete in the singles main draw of the clay court Grand Slam.
Paire retired from his opening-round match while trailing Casper Ruud 6-4, 2-0 on Wednesday with what the ATP Tour said was "dizziness."
This time, Halep and Djokovic each collected a winner's check of about $240,000, but Djokovic got slightly more than she did.
Prajnesh Gunneswaran crashed out in the second round of the men's singles qualifiers of the French Open after losing in straight sets to Aleksandar Vukic.
Conditions in Roland Garros could also have an impact, with the tournament pushed back to autumn because of the coronavirus pandemic.
Dropping only one set all week, Djokovic won his fifth Italian Open title on Monday after beating Diego Schwartzman 7-5, 6-3 in the final.