The new Manchester City right-back believes anything less than claiming the trophy will be viewed upon as an underachievement
Didier Deschamps' men only scraped through to the tournament after beating Ukraine 3-0 in the second-leg of their play-off having lost the first game 2-0.
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Nigeria now lay in wait in the knockout stages, and Sagna says France have only one objective in their minds, while noting the upbeat atmosphere inside the camp.
The right-back said: "As players, we aspire to go as far as possible, to win trophies.
"It would be a failure not to win the trophy. Initially, we wanted to qualify from the group. Now, we want to go step by step.
"There are 11 players who will start, but the 23 are important. The atmosphere is very important and we try to keep this dynamic."
Nigeria claimed their spot in the second round after finishing second to Argentina in Group F, having secured four points following a victory over Bosnia-Herzegovina and a draw with Iran.
“They are the best African team at the moment," said the Manchester City right-back.
"They have very good players. Some play in the biggest European clubs, especially in England.
"They will fight and they have a lot of qualities. But we want to concentrate on ourselves.”
Nigeria have returned to the knockout stages of the tournament for the first time in 16 years and will be looking to become only the fourth African side to make the quarter-final stage.
The two sides will meet at the Estadio Nacional de Brasilia on Monday June 30.