If you drive due west from Paris, heading for the skyscrapers of La Défense, you might not realise immediately that you have left the French capital behind. The Arc de Triomphe remains visible in your rearview mirror. The broad avenue ahead of you is an extension of the Champs Elysées.
After a couple of minutes, if the traffic is not at a standstill, you cross one of the loops of the river Seine and plunge into the tunnel beneath the La Défense business district. You have travelled the length – approximately one mile – of Neuilly-sur-Seine, one of the wealthiest communities in France.
This is the story of two boys who lived, less than a mile apart, in Neuilly-sur-Seine in the late 1960s and early 1970s. They insist that they never met at that time, which is a pity and also a puzzle. By the time they were 17, the two boys shared a common passion. Both wanted to be President of the Republic.
The boys went to different schools but they did have friends in common, three of whom went on to become celebrated French actors. Neuilly was a "village" of 60,000 people in the 1960s, as it is now. People who know the town believe that the two boys must have known each other as teenagers, or at least known about each other, even if they prefer not to remember.
The first boy, Nicolas, was one of three sons of a courageous woman who had been abandoned by her husband, an émigré, Hungarian aristocrat. She brought up her boys in a small apartment beside a flower shop on that broad, noisy avenue leading from the Arc de Triomphe to La Défense.
The other, François, was the younger son of a doctor with extreme right-wing views. To the anguish of his family, the doctor moved François, his brother and his mother almost overnight in January 1968 from Rouen to a comfortable apartment near the Bois de Boulogne, just off that same, busy, mile-long avenue through Neuilly-sur-Seine.
The first boy, Nicolas, lived in Neuilly for most of his life and became mayor of the town at the age of 28. Eventually, he moved along the street which leads, for two and half miles and three changes of name, over the Paris boundary from Neuilly town hall to the Elysée Palace. His surname was, of course, Sarkozy.
The second boy, François, left Neuilly at the age of 19 to jump, brilliantly, through the hoops of the elite colleges which have traditionally led to the pinnacles of the French state. His second name was Hollande.
This Sunday, François and Nicolas, both 57, will probably take the first two places in the first round of the French presidential elections. If so, they will face off in the second round on 6 May – Nicolas as centre-right President and François as Socialist challenger and favourite to depose him.
How strange, and how little mentioned, that they grew up less than a mile apart in the same town. Yes, but also not so strange. Neuilly is not any old suburban town. It is a "power suburb"; a place not only of wealth but influence. It is also the birthplace of another candidate in this year's race, Marine Le Pen, and of someone who might have been the Socialist candidate and might easily have been president, Dominique Strauss-Kahn.
Neuilly is also the home of the country's wealthiest woman, the L'Oréal heiress, Liliane Bettencourt. Her dull-looking mansion, theatre of a political and family soap opera which has gripped France for the last three years, is approximately 300m from the flat where Nicolas Sarkozy grew up.
Neuilly is not France. But it can tell you many things about France. The different relationships of Sarkozy and Hollande with their "home town" can tell you a lot about this year's race; and about the scarcely disguised contempt each has for the other. François Hollande passed his baccalaureate (equivalent of A levels) in the chateau-like buildings of the state secondary school in Neuilly, the Lycée Pasteur. His school friends included Christian Clavier (Asterix in the film) and two other future stars of the comic cinema in France, Thierry Lhermitte and Gerard Jugnot.
Clavier and Lhermitte were also friends of the young Nicolas Sarkozy, who attended Catholic schools a couple of miles away within the Paris boundary.
Hollande went on to Science Po, the celebrated Paris college of political science and the Ecole National d'Administration (ENA), the finishing school for the French political and administrative elite. He joined the staff of the Socialist president, François Mitterrand in 1981 and created a rural base for himself in Corrèze, in the south west.
He became one of the leading figures on the French centre-left for the next 30 years, without ever holding ministerial office. He is a classic product of meritocratic, sheltered educational-political system which also produced Jacques Chirac (on the right) and Lionel Jospin and Ségolène Royal (his former partner) on the left.
This system is detested by Nicolas Sarkozy because he believes that it breeds an inward-looking, cautious kind of politician - but also, perhaps, because it rejected him at the age of 19.
Mr Sarkozy was turned down by Science Po because of his poor English. He trained instead as a lawyer. He leap-frogged into professional politics at the age of 28 by staging a coup to seize the centre-right nomination to be Mayor of Neuilly.
He went on to become a protégé, then an enemy of Jacques Chirac, as Budget Minister and then Interior Minister. He was never part of the traditional French ruling classes, of both left and right: effortlessly superior, understated, sustained by "old money" or the managerial certainties of the "grandes ecoles".
His power-base in Neuilly was a network of wealthy business figures from a "New France" of media and advertising and, mostly, "new" money. Nicolas Sarkozy, like them, became part of an unFrench France: brash, self-promoting; vain rather than arrogant; in-your-face rather than bound by tradition.
The man who eventually succeeded Mr Sarkozy as Mayor of Neuilly, Jean-Christophe Fromantin, speaks eloquently of the imprint of Neuilly on President Sarkozy – both for the good and the bad.
Sitting in the office at the town hall which belonged to Mr Sarkozy for 18 years, Mr Fromantin told The Independent: "Sarkozy was very influenced by the leaders of the world of communication with whom he associated in Neuilly – the pollsters, the advertising executives, the senior journalists... I think he came to see politics as, above all, a question of communication, of transmitting a message, and of controlling a message. That world, that experience, created much of what was best about Sarkozy but was also responsible for the weaknesses which have been exposed in the last five years."
President Sarkozy is unusual among senior French politicians in having no provincial root, real or grafted, in La France Profonde. His political career took him just those two and a half miles from Neuilly town hall to the Elysée Palace.
Even the present mayor of Neuilly says that that was a serious weakness. "Neuilly gave him his conviction that France needs to change in order to survive in the new, globalised world," Mr Fromantin said. "But Neuilly is not France. His experience here failed to give him a gut sense of how people think and feel in the French regions... the profound attachment of French people to their territory, to their traditions, to their soil, to their food to their wine."
It is striking how many of the problems and scandals of Mr Sarkozy's Elysée years have had their origins in his Neuilly years. In 2008, he attempted to impose his press officer, David Martinon, as mayor of Neuilly. His former constituents revolted and elected Mr Fromantin, a local businessman, and independent centre-right politician.
In 2009, President Sarkozy attempted to promote his 23-year-old son, Jean, to the leadership of the political body which runs La Défense, Europe's biggest office development, next door to Neuilly. Since 2010, President Sarkozy has been embroiled in allegations that he accepted illegal campaign funding from the wealthiest resident of Neuilly, Liliane Bettencourt.
Mr Fromantin fears that these scandals have given France – and the world - a warped view of Neuilly-sur-Seine.
"There is more variety here than people imagine," he said. "In any one day, I can meet people in their thirties who have sold an internet business for €100m or a mother living alone with her children in two rooms."
All the same, President Sarkozy remains associated in the eyes of many French people with a certain, distorted image of Neuilly: obsessed with money, full of energy and ideas, not always good ones, and not always in harmony with the rest of France.
François Hollande prefers to forget his Neuilly connections, He stresses his Norman roots or his rural base in Corrèze. His slogan is "le changement, c'est maintenant" ("Change is now").
A change? In fact, if the polls are correct, President Hollande will be a reversion – for good or ill – to an old French tradition: a patrician-intellectual, professional political-manager with a deep provincial taproot.