The United States took silver after Olympic veteran Beezie Madden withdrew due to an injured horse, meaning the United States lost the benefit of being able to drop its lowest score of four riders. Olympic debut rider Lucy Davis had a rail down for four faults.
Germany claimed bronze after its riders returned for a jump-off with Canada to break a tie. Daniel Deusser, the third of four Germans to jump, sealed the deal with a swift and clean round, sparing the final rider from jumping.
Germany, Brazil, the Netherlands and the United States were level going into the final round of the team competition in Deodoro park, while France started the day with two time faults from the previous round of jumping.
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However, its riders left all the rails up to take gold on a tough course, despite scoring time penalties.
Home-team favourites Brazil finished in fifth behind Canada after all three riders still in the competition had a single rail down.
It has been a strong showing in equestrian competitions for the French, who also won the team eventing competition last week.
Wednesday also served as a third qualifier for the individual medal round on Friday.
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