The Super Eagles goalkeeper is looking forward to facing les Bleus in their second round tie on Monday, believing that his side are capable of pulling off a shock win
The west African nation went through as runners up in Group F, earning a last-16 berth despite a 3-2 defeat in their final group match against Argentina in Porto Alegre.
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"We fear nobody," the 31-year-old said in an interview with L'Equipe.
"We have a culture for football. It's our way of life. We work for that and we must show the world what we are capable of.
"France are favourites but anything could happen. I said before the tournament that playing them would be my dream fixture.
"To be honest, we have a great confidence in ourselves."
Enyeama, who has 93 caps for Nigeria, also spoke of his pride at captaining the national side, revelling in the burden of responsibility that the role brings.
"To be captain is one of the most important things in the world," the Lille shot stopper added.
"I don't know what it means in France, but in Nigeria, it means that you carry the team on your shoulders. If all is good, you will be praised - if it's not, you are to blame."
France and Nigeria face each other in the last 16 in Brasilia on Monday.