For the men, Brian Joubert landed two quadruple jumps to become the first Frenchman to win a singles event at a skating competition in Paris.
Kim, 16, who led after the short program, fell once and stepped out of another jump. However, she had five triple jumps to total 184.54 while the three contestants trailing her also fell.
"I was nervous," Kim said. "Before this performance, I was trying not to think about the pressure."
Meissner, 17, fell while attempting a triple axel and singled two jumps.
"Obviously, I know my program didn't go great," Meissner said. "But I was very happy about trying the triple axel."
Skate America champion Miki Ando of Japan finished second with 174.44 points. Meissner was third overall with 158.03.
Joubert won the men's competition with a total of 231.08 points.
Alban Preaubert, also of France, was second with 211.73 and Russia's Sergei Dobrin was third with 193.50.
Joubert opened with a quadruple toe loop and double toe loop. More than halfway through his program, he did another quad toe loop which earned bonus points in the new judging system.
"This is my first Grand Prix of the season and there was a lot of pressure on me because it was in France. I was twice second here and I would have been upset if I didn't win here," Joubert said.
He had a quadruple salchow planned but scaled it down to a triple. His only error was when he stepped out of a triple lutz.
Preaubert had another entertaining program with eight triple jumps, arm swings and swaying to a mix of American music such as the themes from Mike Hammer and Swing Kids. He was third at Skate America three weeks ago.
Also yesterday, world ice dance champions Albena Denkova and Maxim Staviski of Bulgaria took their second event of the season and qualified for the season-ending Grand Prix Final.
The pairs event went to Russian veterans Maria Petrova and Alexei Tikhonov. Americans Rena Inoue and John Baldwin were second. Baldwin has had sleepless nights while here after being diagnosed with shingles, which causes painful blisters and skin rashes.
Denkova and Staviski scored a total of 197.25 points in the ice dance to defeat French dancers Isabelle Delobel and Olivier Schoenfelder, who were second with 194.62.
Italians Federica Faiella and Massimo Scali were third with 176.62.
The Bulgarian couple danced to The Seven Deadly Sins theme.
The top six scorers in each event from the series qualify for the Grand Prix final in St. Petersburg, Russia, next month.