The Irish have never beaten a major side in a game of such importance on foreign soil but will have to do just that in Paris on Wednesday night if they are to reach South Africa 2010.
It looked a tall order before Nicolas Anelka handed the French a 1-0 win in the first leg of their play-off at Croke Park on Saturday evening, and few observers now give the Irish a realistic chance at the Stade de France to overturn the deficit. However, Keane insists Ireland are perhaps at their best when presented with the opportunity to defy the odds and is confident there is a twist yet to come.
Keane said: "Over the years, it suits us probably better because, when we come up against better teams or bigger nations than we are, we always seem to do better against them. We usually struggle when we are the favourites, so hopefully that will be the case.
"We are professionals, we want to win every game. We play football to win and it doesn't really matter what anyone else says outside. You have seen over the years the favourites and there are always upsets, and I certainly believe there is definitely a twist in this game and by no means is this game over, there's no question about that."
A 1-0 victory for the visitors would take the tie to extra time and perhaps penalties. But, while that would represent a major achievement for Giovanni Trapattoni's men, his captain has his sights set on even loftier aims.
Keane said: "I think we can turn it around - we have to believe we can turn it around. I have said in the last few days, believe is a massive word and I think everyone in the squad believes that we can win this game.
"By no means are we going into this game tomorrow thinking we are going to go to penalties. We are going to win the game. Hopefully we will do it in the 90 minutes and, if we don't do it in the 90 minutes, then of course we would take penalties - and, if that was the case, hopefully we would win them."
Keane is one of the handful of men in the current squad to have played at the FIFA World Cup finals - in the Far East a little more than seven years ago. He also suffered the pain of missing out in 2006 and admits that experience has simply increased his hunger for another spell on the biggest stage of all.
He said: "Of course, it was very difficult. Any competition you are knocked out of, the Euros and the World Cup, it's never easy to watch the games. You always think you should be there. But we have got an opportunity now tomorrow to rectify that and hopefully do the job for the team and for the nation, because we certainly deserve a bit of luck."