Elodie Thomis got the fifth-minute winner after entering the area in front of the Colombian defenders and angling the ball into the near corner as the goalkeeper charged from the net.
A draw would have been enough for the French to move on to the next round at the London Games. It will face Group F winner Sweden in the quarterfinals in a rematch of the third-place match in last year's World Cup, when the Swedes won 2-1.
France ended Group G with six points, three less than two-time defending Olympic champion United States, which beat North Korea 1-0 in Tuesday's other group match.
Colombia leaves the tournament without a point or a goal. It needed to beat the French by several goals to have any chance of reaching the quarterfinals as one of the two-best third-place teams.
"We had a good pace the entire match, the only negative was that we couldn't convert on our chances," France coach Bruno Bini said. "But we made it to the quarterfinals and that's the only thing that matters. Now we will just focus on resting and getting ready for the next game."
France dominated from the start and Colombia goalkeeper Sandra Sepulveda needed to make several saves throughout the match to keep the French from getting more goals. Only at the end the Colombians created a few chances. The South Americans also twice were saved by the crossbar in front of about 13,000 fans at the St. James' Park Stadium.
Thomis opened the scoring in a breakaway after a long pass to her from the backfield. She had time to move into the penalty box and choose the corner to place the ball as Sepulveda left the net to try to block the shot.
Thomis played from the beginning on Tuesday after scoring a goal and setting up two others off the bench in the team's 5-0 rout of North Korea on Saturday.
In addition to the winner against Colombia, she twice hit the crossbar, first with a long-range shot in the 26th and then with a strike from inside the area in the 33rd.
Colombia lost despite the tournament debut of Yoreli Rincon, touted by many as the "new Marta." She finally got to play after replacing injured midfielder Catalina Usme in first-half stoppage time.
There had been suggestions back in Colombia of a conflict between the rising star and coach Ricardo Rozo, but the manager said that the 19-year-old forward just wasn't fully fit to play in the previous two games.
With Colombia struggling to control possession, Rincon wasn't able to pose much of a threat during the time she was on the field on Tuesday.
The team's most significant chance came in the 85th when substitute Tatiana Ariza was in front of the net but couldn't get a shot on goal as the defenders came charging.
"We played well in the second half, we showed our style," Rozo said. "That's what we wanted to do from the beginning of the competition but unfortunately we only found our game too late. This is a young team and our performance today showed that we have potential for the future."
Colombia had lost 2-0 to North Korea and 3-0 to the United States. France had opened with a 4-2 loss to the Americans.
The Colombians played without forward Lady Andrade, who before kickoff was suspended for two matches for hitting U.S. player Abby Wambach in the face in the teams' match.
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