A funny thing happened on the way to L'Opera.

Well, truth be told, we were actually walking away from that famously flamboyant French edifice on Saturday afternoon, but let's not get bogged down in the details. Because if you can't use a bit of literary licence in Paris, then where can you?

So there we were anyway, four freshly-fed Scottish rugby hacks, taking the airs on our post-prandial stroll through the centre of the French capital. At which point, things took a rather surreal twist, as we found ourselves sharing a narrow pavement with none other than Eddie Izzard, the cross-dressing comedian. I'd like to say that I was first to notice this fact, but it actually fell to a colleague who, in the sort of voice customarily used by 10-year-old girls at Justin Bieber concerts, shrieked, "It's Eddie Izzard!"

Now it's well-known that Izzard has a few issues with matters of identity, but he probably didn't need to be told his own name. Not at that volume anyway. He smiled wanly, muttered hello and walked off. Well, tottered. He was in heels.

Izzard thus became my fourth celeb spot on the rugby trail in little over a year, joining a club that already included Brian Blessed, Keith Chegwin and one half of The Proclaimers (for obvious reasons, I'm not sure which). I also found myself on the same train as Tilda Swinton but as I wasn't working that day, she doesn't count. Take that, Ice Maiden.

But back to Eddie. Because aside from being a walking wardrobe malfunction, the other thing everyone knows about him is that he once performed a comedy set in French, to a French audience, despite a command of the language that would be flattered by the term 'rudimentary'. It was an incredibly bold move, but it came off. "Bonne courage," the audience cried, not that he understood that either.

In which light, spotting Izzard on a Parisian street suddenly assumed a propitious dimension. Would Scotland do as he had done, take on a French identity and wow the crowds in the Stade de France a few hours later? Would they reprise that famous game of 14 years ago, when Gregor Townsend darted and danced, Alan Tait bulldozed through the middle and Glenn Metcalfe lit up the afterburners? Would they party like it was 1999?

Eh, no, they wouldn't. For as the rain teemed down in that magnificent stadium it was France who decided to go in for a spot of cultural cross-dressing, coming over all Anglo-Saxon in a brutal first half. They pounded at the line. They tried to batter Scotland in scrums. They churned and recycled, recycled and churned. And they ended the period 6-0 behind.

It must be maddening playing Scotland at the moment. Scott Johnson has squirmed at some of the over-the-top praise that has been heaped on his side, but even he has to admit that they are a pretty resilient lot. They turn rugby into a rope-a-dope show, soaking up all manner of punishment before bouncing back off the ropes and throwing a few punches of their own.

Only there weren't enough of them on Saturday evening. Tim Visser struck a late blow when he scored his sixth try in 10 outings a few minutes from the end – when did you last see figures like that against the name of a Scottish winger? It was no more than a consolation score but Visser's try snuffed out France's fitful revival and guaranteed that they would finish last in the Championship table – something else that hasn't happened since 1999.

It brought an extraordinary day, and an extraordinary tournament, to a fitting conclusion. A bit of razzle-dazzle from Scotland as France floundered to the finish.

Eight short weeks ago France were favourites for the title, with most pundits predicting that their closest competition would be provided by Ireland. In the closing moments of the Championship, the only thing left to be decided was which of them would take the wooden spoon.

Of course, in France they argue that la cuillère de bois (as Eddie might say) is only awarded when a team is actually whitewashed in the championship. Well they would say that, wouldn't they? Whether they clear space in their trophy cabinet or not, the fact remains that they have turned this tournament on its head just as emphatically as Wales did when they went from losing eight games on the trot to being crowned Six Nations champions.

And Scotland? Third in the table was a better-than-respectable placing, and a lot better than most of us thought they would do. Their defence has been spine-tingling at times, and it speaks of real collective commitment far more eloquently than any press conference platitude. There was a grim and joyless atmosphere around the Scotland camp last November, and Johnson deserves credit for turning that around.

But they have still enjoyed some mighty dollops of luck along the way. Against both Italy and Ireland they had the good fortune to come up against fly-halves whose effectiveness was severely compromised.

Ireland's Paddy Jackson went to pieces in front of goal, while Italy's Luciano Orquera had an out-and-out shocker. Both played much better at other stages of the campaign.

And Scotland can too. They have gathered the components of a very good game, but it is still in kit form at the moment. They also give the impression they are not quite sure of their style. Still, that never did Eddie any harm.