The French President was eventually forced to abandon the charge in a bid to quell the violence but ended up only firing up protestors keen on getting more concessions from the Government.
A man was being held for questioning over the blaze, Paris prosecutors said.
The police source, however, said numbers were higher, with 21,000 demonstrators taking part in rallies outside Paris. "He wanted to bat it away so it didn't explode by his leg and it went off when he touched it". By 2pm officers had arrested 10 people, they added.
In the south of France police blocked yellow vest leader Maxime Nicolle from crossing into Italy to join forces with Italian demonstrators.
"We mustn't give up", said pensioner Serge Mairesse, from Aubervilliers, just outside Paris.
Another potent winter storm arrives Monday
Residents in Portland and Seattle who are more accustomed to rain than snow waited in long lines to buy shovels and de-icer. Finally, locations to the south of the Quad Cities near Monmouth and Galesburg will see mainly rain through Monday night.
At the march in the southeast city of Lyon, Benard, a 56-year-old computer technician, expressed scepticism about Macron's "great debate" initiative created to address people's grievances. "We'll be here every Saturday of the year if we have to".
About 4,000 marched in Paris, while demonstrations were held in other French cities, including Marseille, Toulouse, and Bordeaux.
French Interior Minister Christophe Castaner has gone on Twitter to express his "disgust" as French yellow vest protesters set alight an anti-terror military vehicle at a protest in Paris.
"We're not children, we're adults", said Hugues Salone, a computer engineer from Paris, among the chanting and placard-waving protesters.
But last week's official estimates were disputed both by march organisers and an independent estimate carried out for news media. Recent polls show Macron's approval ratings rising.
"A Right-wing group of Yellow Vests attacked a Left-wing one, and the result was carnage", one protester who witnessed the confrontation told reporters, according to the Daily Mail Sunday. It was carried out on January 30 and 31.