However limited the roll call of famous Belgians, the country does not give away its citizenship to any old multibillionaire.

An application for Belgian citizenship by Europe’s wealthiest man, Bernard Arnault, the boss of the luxury goods giant Moët Hennessy-Louis Vuitton (LVMH), has been rebuffed by civil servants in Brussels. A final decision is expected in the spring but, according to the Belgian press, Mr Arnault’s application is likely to be rejected.

Mr Arnault – the world’s fourth-richest man, with an estimated worldwide fortune of $41bn – moved from Paris to Brussels a year ago. He insists that, unlike the actor Gérard Depardieu, he has not fled into exile from the high income and wealth taxes in France.

He merely wishes to become a Belgian. Under the existing rules, would-be new Belgians must have lived in the country for three years whether they are penniless Turks or French multibillionaires.

The national agency which deals with naturalisation requests, L’Office des Etrangers, has concluded that there is no reason to make an exception for Mr Arnault.

Belgium is notoriously fussy about the people it allows to become Belgians. Eight years ago, it rejected a naturalisation request from the veteran French rock star Johnny Hallyday, even though his father was a Belgian.

Last weekend, Mr Depardieu, France’s most celebrated actor, announced that he had given up his French citizenship after he was criticised by the government for moving into tax exile in Néchin, a village situated just north of the Franco-Belgian border. The Belgian government said yesterday, however, that it had received no naturalisation request from Mr Depardieu.

More than 500 French citizens – mostly very wealthy – are waiting to hear if they can become Belgians. Applications have increased by 10 per cent since the Socialist François Hollande won the French presidential election in May with, inter alia, a promise to increase income tax to 75 per cent on earnings of more than €1m.

It emerged today that another French billionaire, Alain Afflelou, the creator of a cut-price opticians’ chain, intends to move to London. He said this was to develop new business opportunities and not to avoid French taxes.

Mr Arnault and Mr Depardieu need not despair entirely. A new Belgian citizenship law takes effect next month. In future, ordinary mortals will have to live in Belgium for at least five years before they can apply for a passport. The waiting period will be waived for people with “exceptional merit” judged to have a bona fide link with Belgium.

Mr Arnault had hoped that the Belgian subsidiaries of his LVMH empire would weigh in his favour. Belgian newspapers pointed out yesterday, however, that a formal legal investigation has just begun into some of LVMH’s business dealings north of the French border.

Why Belgium?

Why the sudden French desire to be Belgian? It’s not just the beer, chocolate and moules frites: under existing tax agreements, French citizens who move north qualify for the less onerous Belgian tax regime whether they are Belgian or not. But Paris has indicated it wants to renegotiate this agreement, so a Belgian passport may rapidly become a valuable commodity.