The underdog Colombians opened the scoring in the 19th minute. Andrade broke free from a pair of defenders for a tap-in goal.
Usme clinched her country's first World Cup win with a goal on the counter attack in the 93rd minute.
"We've proved that we're not just here to make up the numbers. We knew that we'd have to play intelligently and fight for every ball. My players are real battlers," Colombia coach Fabian Taborda said of his 28th-ranked team.
The French lost despite outshooting Colombia 21-3 in Moncton, New Brunswick. Much of that was thanks to the play of Colombian goalkeeper Sandra Sepulveda, who made a number of sprawling saves that increasingly frustrated the French attack.
"There were numerous aspects that weren't quite right (Saturday). We weren't accurate enough with our passes at key moments. Despite that, we still created chances, but their goalkeeper had a great match," France coach Philippe Bergeroo said.
France was unlucky as well. Colombian defender Daniela Montoya appeared to touch the ball with her hand inside the penalty area in the 67th minute, but a foul wasn't called.
France wraps up group play against Mexico on Wednesday, while the Colombians face England.
Brazil advances to knockout stage with 1-0 win over Spain
Andressa Alves scored in the 44th minute as Brazil earned a spot in the knockout stage with a 1-0 win over Spain at the Women's World Cup in Montreal on Saturday.
The win is the eighth straight in group stage play for Brazil, which is unbeaten in 14 group matches since a loss to Germany in 1995.
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Spain (0-1-1) controlled the game for much of the first half, but Brazil closed the half with a flurry — capped by Alves' second-effort goal after her first shot was cleared near the goal line.
Irene Paredes nearly equalized for Spain in stoppage time, but her shot off Brazilian goalkeeper Luciana bounced off the near post.
Brazil (2-0) finishes group stage play against Costa Rica on Wednesday, while Spain faces South Kore.
Villalobos' late goal earns Costa Rica draw with South Korea
Karla Villalobos came off the bench to score in the 89th minute as Costa Rica escaped with a 2-2 draw against South Korea at the Women's World Cup on Saturday.
South Korea led 2-1 after a 25th-minute header by Gaeul Jeon and appeared poised to win its first game in World Cup history.
However, Villalobos, who entered as a substitute in the 76th minute, equalized in the closing moments to earn Costa Rica (0-0-2) a second straight draw in Group E. Melissa Herrera scored the opening goal for Costa Rica.
So-Yun Ji scored for South Korea (0-1-1) on a penalty kick in the 21st minute to tie it.
South Korea finishes group play against Spain on Wednesday, while Costa Rica faces group winner Brazil.
England beats Mexico 2-0 at Women's World Cup
Fran Kirby and Karen Carney scored in the second half, and England beat Mexico 2-1 Saturday at the Women's World Cup in Moncton, New Brunswick.
The English moved into a tie with France for second in Group F with three points and a game to go. Colombia is the surprise leader of the group after a 2-0 upset of France.
The 21-year-old Kirby got the first goal of the World Cup for England when she used a toe poke to beat Cecilia Santiago in the 71st minute. Carney scored on a header in the 82nd minute.
Fabiola Ibarra scored in stoppage time for Mexico.
Mexico, last in its group, plays Wednesday in Ottawa against the French, while England will take on the upstart Colombians
