Earlier this week a small flotilla of police boats made its way up the Seine, each one carrying about a dozen players and staff from the French rugby team. The boats moored outside the cathedral of Notre Dame, its occupants put on protective suits and boots, and for the next hour they toured a building that has been closed to the public since the devastating fire that almost destroyed it in 2019. Afterwards, the auxiliary bishop of Paris presented the coach, Fabien Galthié, with the jersey of the Vatican rugby club signed by Pope Francis.

What, do we reckon, was the meaning behind this pilgrimage and the meticulously choreographed ritual accompanying it? A simple photo opportunity? A spot of light tourism on a day off? Almost certainly not. A coach as fixated on messaging and small details as Galthié does not stage these things on a whim. After a planned visit was cancelled in August, the France coach “insisted on” rescheduling it, according to Max Guazzini, the former president of Stade Français who organised the visit.

Galthié is a man of faith, albeit one who wears it as lightly as he must as a public figure in a country wedded to secularism. But there is unquestionably a devotional aspect to his France side, a team steeped in the values of sacrifice and brotherhood and charitable works and, above all, the sense of its own destiny, a sacred mission in which it is playing for something larger than itself. And on a Sunday that will be anything but a day of rest, there is a feeling that this is a French team who are beginning to embrace their calling.

In a way, this is the high-wire act that confronts all teams at a home World Cup. South Africa can talk about treating this quarter-final like any other match. France can scarcely contemplate doing the same. Seventeen million people watched their opening game against New Zealand. Sunday will probably see the biggest television audience for a rugby game in France.

Antoine Dupont’s cheekbone has been one of the main items on the evening news bulletin for weeks. Big screens are being installed in town squares. Black-rimmed glasses have become autumn’s essential Parisian fashion accessory. There’s a madness out there, so do you lock it out or let it in? Is it even possible to do either without losing your own bearings?

“This will be a meeting of quite rare intensity,” says the forwards coach, William Servat. The Springboks have been piping deafening crowd noise into their training sessions in an attempt to recreate the ferocious Stade de France din. Every hit will feel like the end of the world. So how do you hold it together, make sure Ben O’Keeffe keeps his whistle dry, ride the wave without drowning in it? Perhaps, ultimately, it comes down to that sense of mission: the pall of calm that springs from the belief that you are simply telling a story that has to be told.

Certainly it is already possible to glimpse the broader brushstrokes of how this might unfold. It will be relentlessly physical, a game that may well be won and lost at the gain line, where there is perhaps no better team on the planet than South Africa at disrupting and denying the quick ball France need. The return of Dupont restores the enviable array of creative options, and one of the more fascinating subplots will be how much protection France can give his kicking boot – and his face – from Eben Etzebeth and Franco Mostert, perhaps the best kick-chargers in the game.

But the vast stylistic differences that once existed between these two teams are now probably a little caricatured. Over recent months Galthié’s team have become more and more comfortable playing without the ball, while South Africa have become more and more comfortable playing with it. Of the eight quarter-finalists South Africa rank seventh for scrum success and France third. The surprise half-back selections of Manie Libbok and Cobus Reinach, and Jacques Nienaber’s decision to name a 5-3 bench, add still more layers to the game of bluff and deception, portending a collision that – as in the thrilling and thunderous game in Marseille last November that France won 30-26 – will be decided on the finest of details.

Perhaps this should be less surprising when you consider the histories of these two rugby nations. Having only ever met once in the World Cup (in the 1995 semi-final) France and South Africa share not so much a traditional enmity or classic rivalry as a shared curiosity, a cultural cross-pollination that has influenced each in subtle ways. Nine of the Springboks squad have experience of playing club rugby in France, while South African-born talent from Pieter de Villiers to Paul Willemse has been enriching French teams for decades.

For all this, maybe the most telling influence is on Galthié himself. In 1995, distraught at being left out of France’s World Cup squad, he flew to Cape Town and lived in a surf shack while playing for False Bay, the local club coached by a young Nick Mallett. The experience shaped Galthié profoundly, and not just in terms of tactics and ideas. It was while watching South Africa’s triumph in their home World Cup – a competition for which he was eventually called up after an injury to Guy Accoceberry – that he first realised how sport could consecrate and unite a nation, how good teams could be made great through the sensation of tapping into something larger than themselves.

There’s a madness out there, pipe dreams and follies, but it can be your madness, your folly, your pipe dream. Notre Dame was not always the cherished national treasure of a million postcards and tourist selfies. Long before it was mythologised by Victor Hugo and serenaded by Édith Piaf, it lay for centuries in a state of disrepair, vandalised and underfunded. Waiting for someone who could restore it to its destiny.

Perhaps on some scale the story of Notre Dame is the story of this France: feted and romanticised, unloved and neglected, a monument burned down and slowly remade again. It’s a task that defies the imagination. But somehow, it has to be imagined nonetheless.