According to an eyewitness, the victim was injured after the explosion of stun grenades thrown by police at the time when the demonstrators tried to overcome the fence at the entrance to the National Assembly.
As the march continued on its way towards Boulevard Saint Michel, vandals targeted bus shelters, cars and shop windows along the route.
Police said the injured protester lost four fingers as police swooped in to stop protesters from breaching the parliament's exterior.
French Interior Minister Christophe Castaner went to Twitter to express his "disgust" as protesters set alight an anti-terror military vehicle. The police source, however, said numbers were higher, with 21,000 demonstrators taking part in rallies outside Paris.
"It goes back to the fact that there are some profits but they're always to the same people".
"The government has to come out of its virtual reality and enter the real world", said Annamaria Furlan, the head of the Italian Confederation of Workers' Trade Unions Cisl.
"We mustn't give up", said pensioner Serge Mairesse, from Aubervilliers, just outside Paris.
[Teams] Tottenham vs Leicester: Confirmed Line-Ups From Wembley
Trippier's short corner found the unmarked Christian Eriksen and he whipped a pin-point cross towards Sanchez six yards from goal. Replays showed the Colombia defender was just onside as he scored his first goal for Tottenham since his 2017 move from Ajax.
"It's all very good, the great debate, but we want something concrete: fewer taxes, more purchasing power".
"But a lot of people don't see themselves in that and a lot of people have seen what becomes of years of austerity after there was a big economic crisis and now everyone says we need austerity".
In Rome, tens of thousands of people took to the streets to protest the course of Italy's populist government. That was down from the previous week, when official figures put the number at 58,600, 10,500 in Paris.
Several cars were set afire in Paris amid Yellow Vests demonstrations, according to local media. It was carried out on January 30 and 31.
Politicians came together to condemn the arson attack on the home of Richard Ferrand, a close ally of Mr Macron, in Motreff, Brittany.
No one has been hurt and no individual or group has so far been implicated in the incidents.