Sparked by rises in a green tax on fuel, the movement has become a broader protest against the policies of President Emmanuel Macron, who seems determined not to back down.
But there is no formal organisation and most initiatives have been taken on social media.
On Sunday a Facebook page made the call to demonstrate in a week's time.
However, the movement's Toulouse spokesman, Benjamin Cauchy, denied that the call came from the original organisers, claiming that it was probably manipulation by "the far right or the far left".
Regional organisers were discussing the naming of representatives who can "discuss constructively" with the government, he said.
As local authority workers cleared the rubble on the Champs-Elysées on Sunday, a Yellow Vest Facebook page called for an "Act 3" at 2.00pm on the central Paris avenue.
They had been forbidden to march there this Saturday but thousands assembled anyway, leading to clashes with riot police that left 24 people injured, five of them police officers. More than 100 were arrested and 101 detained including a 27-year-old man on suspicion of seriously injuring a police officer in the eye, by throwing metal objects.
To listen to our report from Saturday's demonstration in Paris, click here
Some protesters accused the police of brutality.
Tweet accuses "fascist" CRS of beating demonstrator
À 4 pour frapper un retraité non armé à coups de matraques.Jean Hugon🔻 (@JeanHugon3) November 24, 2018
On parle beaucoup de la minorité de fachos au sein des gilets jaunes, mais il ne faut pas oublier la minorité de fachos au sein des CRS.#GiletsJaunes #24Novembre pic.twitter.com/BdTcLOep3e
The call for a new demonstration said there should be "no vandalism, but five million French people in the street".
Its demands were "1) more spending power, 2) scrap fuel taxes" and added "otherwise, on the move for Macron's resignation".
This Saturday's protests attracted 106,301 people, according to official figures, less than half the number who turned out across the country the previous week.
Most of the protests outside Paris went off peacefully, although one gendarme was seriously injured and two others slightly hurt in the Channel port city of Calais, leading to four arrests. More violence was reported in Villefranche-sur-Saône, central France.
Two journalists from the BMTV 24-hour news channel claimed to be victims of an "attempted lynching" after being abused and threatened by several dozen protesters who chased them away from the scene of the protest in the south-western city of Toulouse.
TV crew attacked in Toulouse
They have filed complaints with the police, as has a reporter from CNews TV, who was kicked and spat on while covering the rally in the southern town Béziers.
The Reporters Without Borders press freedom campaign on Saturday issued an appeal to the Yellow Vests not to aim at the wrong target by harassing journalists.
It cited several cases in the preceding week, particularly targeting BFMTV, one of whose journalists had an egg broken on his head while reporting live from a demonstration.
Meanwhile, US President Donald Trump tweeted his own idiosyncratic comment on the movement.
The large and violent French protests don’t take into account how badly the United States has been treated on Trade by the European Union or on fair and reasonable payments for our GREAT military protection. Both of these topics must be remedied soon.Donald J. Trump (@realDonaldTrump) 25 novembre 2018
Macron on Saturday evening said he was ashamed of the violence on the Paris demonstration, although Interior Minister Christophe Castaner later commented that most of the damage was to property, not people.
Attending the EU summit to discuss Brexit on Sunday, the president had little to say on the protests, apart from acknowledging that European politicians had to "provide meaningful economic, social but also cultural answers" to "our middle and working classes".
Budget Minister Gérald Darmanin was more forthcoming, hinting that the government could cut taxes further but warning that would mean a moratorium on public spending.
Economy Minister Bruno Le Maire, for his part, announced that he was organising a meeting on Monday of business representatives to assess the impact of the protests, which have often involved pickets of supermarket entrances and transport hubs, on sales.
Macron is to organise a summit on climate change, according to theJournal du Dimanche newspaper, in order to calm the debate on energy policy and its effects on taxation.
Réunion curfew lifted
Officials lifted a curfew in the Indian Ocean territory of Réunion on Saturday, saying that violence by gangs of young vandals had subsided.
Since 17 November 143 people have been arrested, they reported.
Public transport was still not running on Sunday and the airport was to close at 4.00pm local time.
Unemployment on the island is 22.8 percent and 40 percent of the population live below the poverty line.