Kerber appeared to get back into the match when she recovered one break but the German immediately dropped her serve again.
She has not yet defeated a top 20 opponent this year, and while she has reached one final so far this season, she lost that one to Anastasia Pavlyuchenkova in Monterrey.
Seeded winners in the women's first round: No. 6 Dominika Cibulkova, No. 8 Svetlana Kuznetsova, No. 15 Petra Kvitova, No. 30 Timea Bacsinszky. "On the other hand, maybe that is just what she (Kerber) needs, because it will make sure that she is concentrated right from the start".
The 38-year-old Ivo Karlovic, who is also known for his big serve and 6-foot-11 (2.11-meter) stature, advanced to the second round with a 7-6 (5), 7-5, 6-4 win over teenager Stefanos Tsitsipas.
"I think it doesn't really matter how I played, but I won", the 15th-seeded Kvitova said.
Several of the big names in the sport will not be at this year's tournament. The 2016 women's champ, Garbine Muguruza, will also be in action, facing 2010 French Open victor Francesca Schiavone.
Petra Kvitova made an emotional and victorious return to tennis on the opening day of action at the French Open but world number one Angelique Kerber was knocked out. So even if I'm No 1, No 10 or whatever, I have to fight for my wins for my matches from the first point.
Kerber has not been playing well, and she came into the French Open with little confidence that she'd fare well on clay. "And just, you know, going out and trying to find my game", she said.
Puig won 6-3, 3-6 and 6-2 over Vinci in an hour and 50 minutes while the 32-year-old Argentinian made a 7-5, 6-3 and 6-4 over Mannarino.
"She (Williams) is much more experienced than me, and she knows how to handle some crucial points well", said Wang, adding she would play better on clay next year.