The ground is quiet now, but only 12 hours earlier it had been a seething cauldron of passion and noise as Clermont Auvergne claimed a thunderous 22-16 victory over arch-rivals Toulon, clinched with a ferocious surge in the final few minutes. The result took them to the top of the Top 14 table, in pole position with just four games left before the play-offs. Staggeringly, it was their 74th home win on the trot.
The view from Vern Cotter's roomy office in the stadium's north stand looks out over the Michelin factory, an ever-present reminder of the club's roots as the tyre company's works team. The club actually began life - in 1911 - as the Association Sportive Michelin, but league rules demanded a name change, to AS Montferrand, a few years later. Even now, its full name is Association Sportive Montferrandaise Clermont Auvergne, and Cotter likes it that way. He likes the fact the club has roots, its feet firmly planted in the volcanic soil of the Massif Central.
More of that in due course. Cotter is a sharp man who understands the nuances of such things, but for the moment his brow is furrowed by concerns over the details of the performance against Toulon. Yes, they won, but it was a slapdash performance as they allowed the Provencal side to come back from a 13-0 deficit to draw level, 16-16, just as the match entered its final quarter.
It took two calm penalties by Morgan Parra, and a helpful miss by Toulon's Jonny Wilkinson, to keep Clermont's run of home wins, which began in 2009, on course.
The indications are that Cotter has been at his desk for a couple of hours. He has reviewed the video footage of last night's game, made his notes, and has already issued the instruction to his players to come in for an extra session on Sunday. "It's usually their day off," he says firmly, "but there are a few things we have to sort out."
It was ever thus at Clermont. The perennial bridesmaids of French rugby, they contested 10 French championship finals before finally winning their 11th, under Cotter, when they beat Perpignan in 2010. It was a triumph that was meant to shatter the hoodoo, but it returned with a vengeance last year when, as red-hot favourites to beat Toulon in the Heineken Cup final in Dublin, they snatched yet another defeat from the jaws of victory and handed the prize to their opponents.
It was not the only thing that went wrong for Cotter last May. By then, he had already struck an agreement with the Scottish Rugby Union to take over as Scotland head coach, but his hopes of an early release from his contract with Clermont were scuppered when the French club's president made it clear he expected the New Zealander to honour it in full, and stay for another year. If Clermont supporters feared then that Cotter would drift through this season, that his appetite for success would be gone, they underestimated the man who has transformed the culture of their club over the past eight years.
That and the impact the defeat in Dublin would have on him. "We were all pretty devastated after losing that final," Cotter recalls. "We had pushed hard at the start of the season with the idea of winning the Heineken Cup and I?¯still say that we were the better team in the final.
"It's just unfortunate that [referee] Alain Rolland didn't see things in the same way as we did for the last few minutes."
The setback clearly affected Cotter deeply. It also dynamited Clermont's French championship chances, for they were still reeling from their Heineken heartache when they lost feebly to Castres, who would go on to take the Top 14 title a week later. But as the new season dawned, he and his players determined amongst themselves that they would make amends.
With just a few weeks of the campaign left, Clermont are in the driving seat domestically, and a Heineken Cup quarter-final at home to Leicester Tigers in 10 days' time means that European glory is still on the cards as well.
It is a poignant time as well, though. Cotter's reign is nearing its end and a host of stalwarts will be leaving the club when the season is over. Nathan Hines, Sitiveni Sivivatu, Regan King, Lee Byrne, Gerhard Vosloo and a few others are moving on. Yet, ever the pragmatist, Cotter is determined that a veil of tears should not obstruct their vision of what they still want to achieve.
"At the last home game there is a tradition that all the players and people who are leaving the club stand up in the middle of the paddock and say their goodbyes," he explains. "But I?¯don't want that to dominate the next few weeks.
"I want us to go as far as we can this season. I'm not going to let those kinds of things steer us away from the objective, which is to go as far as we can and try to win something.
"But it will be tough. It has been a real rollercoaster ride for us all here. We've lost three finals but then we won our first one and we have achieved some pretty good things.
"We've been recognised as a European team, which wasn't the case beforehand and people have grown within the group. The club has grown and I've seen players develop, arrive and leave, get married. It's been a long time and it has not just been a job. It's been more than that.
"But we're not getting sentimental about it. We're not going to have players saying 'this is my last time'. We're just going to come together and say 'this is what we want, we want to win the Heineken'. We may or may not, but that desire has got to be there.
"As we're getting towards the end of the season, those experienced guys will want to stand up and go as far as they can."
But has Cotter done that? He has brought solidity and consistency to Clermont, made them a club that is both respected and feared, and ended their trophy drought.
But he has pledged to leave them with business still to be done, jobs still to be finished. And he is also leaving to take charge of a side that, to be brutally frank about it, is in a bit of a state at the moment.
Cotter is adored by the Stade Marcel Michelin faithful. Many are baffled by his decision to go.
The conventional view is that he sees Scotland as a stepping stone on the way to fulfilling his real ambition of coaching the All Blacks.
Fair enough, and Graham Henry did something similar as he took charge of Wales before heading home to New Zealand, but there are more reliable ways of enriching your cv than spending time on the Murrayfield payroll. There is also the question of why anyone would swap the weekly adrenaline fix of running a team at the top of the French league for trying to arrest the slide of one that is well down the international pecking order.
"It's tough to leave," Cotter admits. "But nothing's forever. I?¯think I?¯always challenge myself to come up with something new and develop things. I?¯just think it is a time to move, to move on.
"I?¯don't know if it's a feeling or an instinctive thing, but the choice was made to go to Scotland. That was something we wanted to do. It was perhaps something we didn't need to do, but we wanted to do. Test rugby has always been something I've wanted to experience. A World Cup as well. These are things that might be once-in-a-lifetime experiences.
"This opportunity presented itself and I'm really looking forward to experiencing rugby at its highest level against the best teams in the world. I'm sure it will be a learning curve, but I'll trust my ability to adapt and challenge myself and challenge the people around me."
So what can those people expect? One exchange sums it up.
I?¯raise the point that he has a reputation as a hard taskmaster. Does he think it is fair?
"I?¯think I'm fair," he replies.
But he's ducking the question. I ask again if the reputation is fair.
"I?¯think it's probably fair," Cotter concedes. "I?¯don't like cutting corners. I?¯like to see the whole job get done. It doesn't mean I?¯don't have an open view, because I?¯have a very open view of things, but there are negotiables and non-negotiables when I'm coaching. We'll draw the line in the sand quite quickly and we'll work from there."
Cotter refuses to expand on the non-negotiables - "We'll keep those within the team" - but he puts heavy emphasis on the qualities he likes to see in players. He likes honesty. He likes trust. He likes loyalty. He likes open communication and confidence. "If you have these things you have the ingredients to be successful and you have the base to work and move forward," he says.
Cotter's two public appearances at Murrayfield last year were not exactly soaraway successes. The first, in May, saw him thrust into the media's baleful glare just as the storm surrounding his contractual spat with Clermont was building strength, and it hardly helped that nobody appeared to have briefed him on the latest developments in that saga. Then, in November, he sat stony-faced through a press briefing, refusing to answer questions in anything but non-committal terms.
On his own ground, however, Cotter is more talkative, more engaging, more likeable. In Scotland we have become too familiar with coaches who have graduated from the school of snake-oil salesmanship, but Cotter is certainly not one of those.
"I'm just a Kiwi farmer," he says at one point, a claim that acquired literal truth a little while ago when he purchased some land next to the farm on which he grew up.
When he talks warmly of Clermont it is clear that it is the club's grounded culture that pleases him most. "This is not a flamboyant part of the world," he says. "It's not on the coast; the people are not transient people. It is traditionally a working-class town and the community around it is rural. People are attached to the land."
Cotter will step into the Scotland job on June 1. Within days, he will be on a Transatlantic flight, leading the team on a four-Test tour that will take them to the USA and Canada, and then later to Argentina and South Africa.
It is a mind-addling schedule, a dive straight in at the deep end.
He is canny about his hope for the venture. "You have to seek to understand before being understood," he says. "So I'll be listening a fair bit, just hearing what people have to say and how they see things. At least I'll get to know them pretty well."