The fans might have drunk Dublin dry that evening, but many of the players had a different attitude.
Their indefatigable captain, Jim Aitken, for instance, wasn't interested in resting on his laurels. "Most of the alickadoos [officials] at Murrayfield thought that was it after the Irish victory. I knew that a couple of them were saying that it wouldn't matter if we didn't beat France, because we'd already had a great season," recalled Aitken. "I replied that it would be a disaster if we lost the last match. We had to finish the job."
Nobody was under any illusions it would be straightforward. The earlier performances of Les Bleus had left the England hooker, Peter Wheeler, describing them as "unbeatable". Yet, with Jim Telfer determined to pull off another masterstroke, and such test-class performers as John Rutherford, Iain Milne, David Leslie, Jim Calder, Iain Paxton and John Beattie committed to the cause, there were reasons to be optimistic, not least considering the French had struggled on their recent trips to Edinburgh almost as much as the Scots had toiled after arriving in Paris.
As in 1990, it was a winner-takes-all situation and the Scots knew their opponents would fly out of the blocks and serious questions would be asked of their defence. But these were tough men; a dozen of the squad were from the Borders and many had grown up battling against one another.
"If you had gone to Mansfield Park or Netherdale and listened to the crowd hurling abuse at you and their guys getting stuck into you, then you weren't afraid of anything in rugby," Rutherford pointed out. "I think there were occasions when we played better than we did in 1984, but we needed to show we could tough it out when necessary and we did."
The hosts were certainly under the cosh in the early stages, with such talismanic figures as Jerome Gallion and Serge Blanco orchestrating their own brand of improvised magic. Time after time, it seemed as if their artistry would unlock the Scottish fortifications, and Gallion managed to secure a try, which put his side 6-3 in front at the interval. But, considering how much they had dominated, it was a fragile lead for the visitors. Worse still, from their perspective, they gradually fell foul of the referee, Winston Jones, and Peter Dods was in impeccable form to punish their lack of discipline. Then, on the hour mark, they lost the influential Gallion to injury in controversial circumstances.
"He was kind of high-tackled by David [Leslie] at a line-out," said Telfer. "David clattered into him and he was carried off and the French were never the same." That view wasn't shared by his skipper. "They didn't lose the game because of Gallion," said Aitken. "They were already beaten by then. David just ran into him - I would like to think it was intentional, but I don't think it was. Anyway, we were playing with them at the end."
The importance of the often underrated Dods should not be ignored. He gradually clawed back the deficit, then with the tussle on a knife-edge, the Scots moved in front with a try that encapsulated all the qualities they had displayed throughout the campaign.
"Blanco was caught under a high ball and driven some way back downfield," stated Telfer. "The impetus that gave us was crucial, and we scored from more or less the next line-out."
Suddenly, Murrayfield erupted in a cataclysmic outpouring of emotion and, although some of the Scots were tired by this stage, that was nothing compared to the fashion in which the French were both dead on their feet and less concerned about playing rugby than going around punching opponents. No matter.
The metronomic Dods kept landing kicks and, despite having a badly swollen eye, his vision was spot-on when he sealed the outcome with his fifth penalty, which sent his side 21-12 ahead. That was enough. At the climax, Aitken's men leapt in the air with joy, the supporters invaded the pitch, and there was jubilation and no little incomprehension.
"None of us had any experience of winning a grand slam - Scotland has last done it in 1925 - so we were both overjoyed and amazed at the reaction," said Rutherford, while Telfer, who had questioned his abilities less than a year earlier, following a humbling defeat for the Lions in New Zealand, added: "At the finish, there was an air of disbelief. It was an incredible achievement," said the coach. "These things just didn't happen to Scotland."
The post-match dinner, by all accounts, was a messy affair. Edinburgh rocked, Glasgow gallivanted, and, for a few days, rugby was all over the news.
But, perhaps in keeping with Scotland's rapidly fluctuating fortunes, the caravan quickly moved on. Aitken retired after 1984, Leslie was never quite the same irresistible force again, and, most significantly, Telfer stood down at the denouement of that glorious season.
The consequence was that, in 1985, the SRU's finest came away with only one prize - the wooden spoon - although they lost three of their four fixtures by less than one score. That precipitated wholesale changes and the unearthing of a new crop of talent, including the Hastings brothers, who were eventually involved in the grand slam of 1990.
But, for the moment, let's just pay homage to the heroes of '84.