Last year, the head of the French state railways, Guillaume Pepy, cited this law as the reason why Sarkozy had never travelled by train.
With an average of two bridges per kilometre, a presidential journey from, say, Paris to Lyon would require 900 police officers to be deployed.
How, then, did Hollande, accompanied by the Spanish Prime Minister, Mariano Rajoy, manage to travel on a scheduled high-speed train from Paris to Brussels for the European Union informal summit last Wednesday? Both SNCF, France's state-owned rail company, and the Elysee Palace said the security arrangements were "confidential".
But it is understood that Hollande has given instructions for the 60-year-old law to be ignored until it can be removed from the statute book. This meant that there wasn't a police officer beside every bridge between the Gare du Nord and the Belgian Border.
The Elysee Palace put the cost of the trip for Hollande and his entourage at €5972 ($9790). The cost of travelling to Brussels in two presidential executive jets, as Sarkozy did, is estimated to be 10 times higher at around €60,000.
Hollande returns home each evening to the flat in the unfashionable 15th arrondissement which he shares with his partner, Valerie Trierweiler, and her teenaged sons.
Because the flat has windows on the street, security chiefs regard it as a security risk. They have also pointed out that the presence of the head of state could cause disturbances for Hollande's neighbours. But Hollande has decided to test this advice rather than accept it.
The "Monsieur Normal" act - and his frenetic first two weeks in office - have gone down well with French voters.
An Ifop poll put his popularity rating at 61 per cent, the third highest for any newly elected President in half a century.
- Independent