Today's match against Saudi Arabia finds Rieper and his goalkeeper a picture of unity, harnessing those fierce competitive instincts in their country's cause. As the Celtic and former West Ham player puts it: "The old Olympic spirit, being happy just to take part, is no longer good enough for us Danes."
Following the departure from Scotland of both his compatriot, Brian Laudrup, and Paul Gascoigne, the vastly experienced Rieper goes into the finals as arguably the Scottish game's top player. With his 30th birthday having fallen five days before France 98 began, it may be now or never for him to make a significant impact on a less parochial stage.
That is not to imply that he is an international under-achiever. Denmark's victory in Scotland in March brought his 50th cap, 31 of which came in consecutive matches, a Danish record. However, Rieper was too young to be involved in their previous appearance in the finals, in Mexico 12 years ago, and did not make the squad which became European champions in 1992.
That was a setback, certainly, yet Rieper's background is not the kind to lead him to confuse disappointment with disaster. Although he began playing at the age of five for his home-town club, Aarhus, he was "never desperate" to follow his father into a playing career - "I was into everything - athletics, basketball for the national team - but I carried on playing for the Aarhus youth teams and eventually the football thing clicked into place."
Even after he made his choice, he went to university where he majored in sociology. Later he worked as an estate agent ("Not the dodgy profession it is here," he assures me) while stopping strikers at weekends. "The Danish system gives young players a balanced perspective on life. If they fail at football, it's not the end of the world. It has also given me a balanced perspective on things and helped me cope with the pressures of the British game, which can be intense."
Rieper first played for Denmark in 1990. A move to Brondby, the club where Schmeichel and the brothers Laudrup came to prominence, ought to have confirmed his place in the national set-up. Instead he fell out of form and favour. "The training was full-time, which I found very, very hard. I didn't perform well, and then I was asked to fill in up front. I was happy to do it but it isn't my position."
The downturn in Rieper's fortunes proved ill-timed indeed. On the eve of 1992 European Championships, Yugoslavia were expelled from the tournament and Denmark invited to replace them. "The boys were complaining that they wouldn't get their summer holidays! But it turned out to be the best experience of their lives," Rieper says. "Me? I stayed at home and watched it on TV. It was an emotional and exciting time to be Danish. There was great pride in what a little country without great resources can achieve."
The suspicion remains that it was a glorious one-off. After all, the seemingly more talented "Danish Dynamite" side of 1986 imploded in the second round of the World Cup. "We've got to be realistic and accept that Denmark aren't going to win championships regularly," Rieper says. "We've got around 30 players that could possibly perform at this level. Italy, Germany and England may have 100. But I'll be surprised if we slip up in the first phase."
They ought to go through from a group also containing South Africa and France, whom Rieper ranks as favourites along with Brazil, Italy and Germany. Not England or Scotland? "No," he replies, eschewing the platitudes endemic in his profession. "People have very high expectations of England in particular, but I believe they're too high. Look at Manchester United in the European Cup. They are one of the best teams in Europe, but English sides always peak too soon, in the autumn and Christmas."
He knows about the British game, having had "three good years" with West Ham before August's pounds 1.5m transfer to Celtic. His partnership with Alan Stubbs was a key factor in ending Rangers' rule, but Rieper's satisfaction with the way the move has worked out extends beyond the addition to his medal collection.
As one who enjoys travelling and, like Jurgen Klinsmann, used to go on backpacking holidays, he likes the idea of sampling different cultures. He had heard "a lot of negative things" about Glasgow but admits to being "pleasantly surprised".
Language has not been a barrier, either in the international Celtic dressing- room or in Scotland at large. Anyway, Rieper has an interpreter. "My daughter couldn't speak Danish when she started nursery. Now she's picking up Scottish phrases and mixing it all up."
And the Glasgee cuisine? "I would never eat haggis if you paid me," he says, simultaneously laughing and squirming. Being able to socialise with Brian Laudrup, when he was across the city at Rangers, enabled Rieper to keep in touch with his roots. Now the Old Firm rivals, together with Schmeichel and Michael Laudrup, represent the spine of the Danish side in France.
While pundits point to the Laudrups as the players who could make the difference, Rieper is convinced that Schmeichel is the one player they could not afford to lose. "Peter's the best keeper in the world. The defender who wouldn't want him behind him is a fool."
That did not, of course, stop them falling out so photogenically. "It was against Portugal in a European Championship qualifying game. Two minutes from time, this ball came into our box and I could have got it away easily. Then Peter charged out and got me, not the ball."
Yes, but what were you saying to each other? "It's not nice," Rieper explains. "You couldn't print it."Reuse content