One of the reasons police are particularly worried is that, unlike most street protests, they do not know exactly what to expect.
A police source said that more than 1,500 protests are expected but only a hundred have been declared with the local authorities so far.
“It's a real headache: without declarations, the local authorities cannot make a specific request for police reinforcements, nor know how many police forces are needed, and where,” a police source told AFP.
In fact because all of the protests have been organised through social media, the French authorities fear the location of the protests is almost impossible to pin down and it makes it difficult to predict how many people will turn up.
Philippe Capon, general secretary of the UNSA Police union told BFMTV
: “The problem is that we do not really know what will happen.
“Usually, when traditional social movements are organized, they are declared with the local authorities.”
Another of the reasons the French police — most of whom have dealt with more than their fair share of protests — are particularly worried is that the 'yellow vests' do not have an officially identified leader, spokespeople or political affiliation.
On top of that they aren't linked to France's traditional trade unions, who normally organise protests through their central and regional structures.
Capon said that Saturday will be “complicated”, in particular because of the lack of spokespeople.
“Without a point of contact, it is complex for the police to establish an exact program and anticipate events.”
“It's the kind of movement that spreads like a spider's web,” said Capon. “This lack of opportunity to anticipate, it complicates our task a lot, and it greatly increases the risk of overflowing.
“Because we know from experience that each event brings its share of 'parasites' who just come to make trouble,” said Capon, adding that this is especially true when you arrange a protest on social media.
“When you call people you do not know to join you, you do not control these people, you do not know who they are or how they will react,” he said.
The Interior Ministry said on Thursday that a monitoring unit would be set up in conjunction with the Ministry of Transport, and that 30 units of mobile police forces would be made available to the local authorities.
The French police have the power to “evacuate by force any unauthorized protest that impedes traffic” and offenders could incur up to two years in prison and €4,500 in fines.
What do we know about the organisers, so far?
Investigators working for the central territorial intelligence services (SCRT) believe they have identified eight organisers, five men and three women aged 27 to 37 years, from their Facebook accounts.
All of them except one live in the Seine-et-Marne department in the greater Paris region of Ile-De-France.