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The Sketch: Two leaders, united by fiscal embarrassment and mutual mistrust

They met outside one of our great aristocratic town houses, attended by our golden-breasted guardsmen. Later, amid the glittering gold leaf inside – and watched over by topless angels – the leaders signed the two treaties. (They're expensive, these signing ceremonies – we did two-for-one.)

"A shared history," David Cameron said. We were going into a 50-year nuclear partnership with France and our PM assured us it was on the basis of our shared history. Blimey you don't want to bring that up!

So, Nick Robinson did. If there was a crisis in the South Atlantic, he asked, would we be able to borrow the French aircraft carrier to sort it out? Nicolas Sarkozy rolled his shoulders, flashed different parts of his strangely feminine face at us and said: "It would take a hell of a crisis." That was probably true. "Do you imagine our British friends facing a crisis and France folds it arms and does nothing?" We didn't imagine that, any of us.

Though doing nothing would be an improvement on selling Exocets to the enemy, to be sure. M le Président looked round at us in the way we all admire and asked: "What idea do you have of France?" There's more than one answer to that, but it wasn't the time or place.

However, you could tell there was a submerged sense of unease in our new friend about "our shared history" as he described the next question on the British rebate as "slightly perfidious". Ah yes, in our shared history there it was: the ancestral insult.

Perfide Albion betrayed France out of its global inheritance; cunningly we won all the wars, treacherously we invented industrial production, perfidiously we held the line against the Nazis...

Whatever our passing leaders say, our national narratives chatter in the background saying the same sort of things over hundreds of years.

To cover over this inconvenience, Sarkozy span us a number of genial lines. "The fact is, Britain is France's closest neighbour." (It isn't). "Our values are the same." (They aren't); "When Britain succeeds, it is a success for Europe." (Pull the other one, chum.)

So, to the point. Would he stand shoulder to shoulder with Britain over the rebate? If he'd been wearing a monocle like his periwigged antecedents he would have opened his eye and let it fall. As it was he did the trick with his ear and the translation earpiece fell out. It lacked elegance but it made his point. "Five years is a long time. Can you trust the French for 50 years?" ITV asked the PM. The correct answer is a question: "To do what?"

Cameron may not be here in five years and neither of them will be in 50. Much of this entente frugale depends on the personal qualities of them both and no doubt on the new frugality.

What happens to our nuclear amours when it all passes?