The shoe in question belongs to Beatrice, my daughter's best friend, aged five. Every other Friday, Beatrice, who is half-Irish and half-Swedish, comes to lunch and to play at our home. School lunchtimes are so lengthy in Paris (two hours), and the weekends so crowded with family activities, that the social life of Parisian children occurs largely in the middle of the school day.
Every second Friday afternoon, the two girls are taken back to school by our Filipina occasional baby-sitter, Rowena. Like most of the foot soldiers in the large army of Filipinas in Paris, Rowena hardly speaks a word of French.
Last Friday, the trio were getting off the Metro when Beatrice's shoe detached itself from her foot and fell between the train and the platform. Beatrice was distraught.
The two little girls approached the woman in the ticket office and told her the sad story. The ticket office woman was, by all accounts, charming. She made a telephone call and an engineer arrived. He ordered the current of Line Six cut off for 20 minutes. Trains stopped; passengers spilt out; others joined them. Nothing and no one could move until the shoe was recovered.
The Metro is not the London Tube, where waiting 20 minutes for a train is normal. Parisians are used to catching a train within two minutes.But when the station staff pointed out the problem no one complained. It was accepted, with good humour, that this was an entirely proper reason to shut down Line Six.
Three weeks' earlier, the whole of the underground and bus system had been closed for two days after a Metro security officer collapsed and died on the job from natural causes. The employees of the Parisian transport company went on strike insisting - against all the evidence - that the man had been assaulted by two illegal jewellery vendors. Parisians, for the most part, tolerated this absurd strike with resignation and good humour. In neither incident - the shoe or the strike - could such forbearance be expected in London.
The piano in question belongs to my wife, Margaret. Several months' ago, she started to play again after a 20-year interval. Last week she got into the lift with an elegant, hatchet-faced, sixtysomething woman who lives above us. She has never shown any interest in talking to us.
Abruptly, she asked: "Is it you who plays the piano?" My wife admitted that it was. The woman looked her in the eye and said: "You're not making any progress, you know."
Such first-degree, premeditated rudeness could only happen in Paris. Foreign visitors often assume it is aimed at them. It is not. Parisians are equally rude to one another.French friends say it goes back to the Second World War, or even the Revolution, when neighbours often betrayed one another to the authorities.
A lawyer friend reports that neighbour-versus-neighbour court cases are one of the great boom areas of the French legal system. One recent case concerned an excessively loud coffee-grinder.
So there is the paradox. Parisians can be tolerant, almost to a fault. In their attitudes to strikes, dog-dirt, little-girl's shoes fallen onto the Metro tracks, they display an almost Buddhist resignation.
And yet in their personal relations, they have a breath-taking capacity for waspish and often arrogant defence of their personal space.
When the shoe was finally restored to Beatrice, the two girls were more than half-an-hour late for afternoon school. The big door was shut. The school's security officer came out and screamed at them to go away. The school rules stated, she said, that once the door was closed no one could be allowed in.
Clare put her hands on her hips and screamed back. It was not her fault - it was not even Beatrice's fault. She didn't want to go home; she wanted to go to school. The two girls were admitted.
One sharp tongue had recognised, and bowed to, another. After two years, little Clare has become, for good or ill, a Parisienne.