'Graffiti was being scrawled on the statues and walls around the parliament building, but nobody got over the railings.' Police responded with baton charges and tear gas around the Champs Elysee after demonstrators threw stones at officers and vandals tried to smash shop windows.
Paris police said the man had lost four fingers.
French Interior Minister Christophe Castaner went to Twitter to express his "disgust" as protesters set alight an anti-terror military auto.
Police said 31 demonstrators had been arrested in the unrest.
"Nothing justifies intimidations and violence toward an elected official of the Republic", said Macron, in a tweet in relation to the incident.
"We mustn't give up", said pensioner Serge Mairesse, from Aubervilliers, just outside Paris. This was the 11th time he had marched with the movement, he said.
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.
"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".
Protests also took place in other French cities, including Marseille, Montpellier, Bordeaux and Toulouse, the BBC noted.
On Feb. 5, France passed an "anti-casseurs" (anti-hooligan) law banning protesters from hiding their faces, giving police greater powers to extract potential troublemakers from demonstrations, and granting local authorities the right to ban individual protesters.
Interior ministry figures issued at 2pm put the turnout across France at 12,100, of whom 4,000 marched in Paris, down on the previous week's figures.
Politicians from across the political spectrum condemned the arson attack on the home of Richard Ferrand, a close ally of Macron and president of Parliament's Lower House.