In the men's draw, world number one Novak Djokovic strolled into the fourth round with a 6-3 6-3 6-2 victory against Italian qualifier Salvatore Caruso.
Halep next faces Poland's Iga Swiatek who celebrated her 18th birthday by seeing off Olympic champion Monica Puig 0-6, 6-3, 6-3.
It was the first time since had played three matches in a tournament since the Australian Open in January and the 37-year-old, who has had a knee problem, looked desperately short of fitness and form.
"I played my best tennis and I hope it continues", said Siniakova, who was the women's doubles champion in Paris in 2018 alongside Barbora Krejcikova. Her first major back was last year's French Open, where she withdrew before a fourth-round match because of a chest muscle injury.
The top seed and reigning USA and Australian Open champion, crashed to a straight sets defeat, going down 6-4, 6-2 to the Czech who was ranked 42nd in the world before the tournament started. "I can also do what I want".
Williams said after Saturday's loss that she wasn't fully match fit.
Barty overcame the disappointment of dropping her first set of the tournament to subdue her free-hitting but temperamental opponent with 11 aces and 25 winners. It was Williams whose strokes were off target: Her 34 unforced errors were twice as many as Kenin's total.
Kenin wasn't even born when Williams made her Paris debut in 1998.
Wawrinka, the 2015 champion and a three-time major victor, recorded his 500th match win with a 7-6 (7-5), 7-6 (7-4), 7-6 (10-8) win over Grigor Dimitrov. Siniakova got 67 percent of her first serves in play and saved all seven of her break points. "It's wonderful. It's the thing I couldn't believe", said Siniakova, who will face 2017 U.S. Open runner-up Madison Keys next.
'I feel like I have had some great runs last year, and I'm hoping to still build on that this year and keep it going'.
The nerveless youngster from Pembroke Pines, Florida saved a break point and on her second match point Williams went long.
"Clay is one of the Grand Slams, and I have to figure out how to sort of embrace it and love it in my own way. But it's just been a really grueling season for me".
"I think it was really good and it was working and I think her serve today wasn't so good".