Masked men threw projectiles at police, who responded with tear gas and stun grenades.
Relations between France and Italy sank to a new low last week when Paris recalled its ambassador, citing meddling in domestic affairs after Di Maio met with senior figures of the Yellow Vests movement in France.
The protest in the French capital has passed the National Assembly and will end up near the Eiffel Tower. The police source, however, said numbers were higher, with 21,000 demonstrators taking part in rallies outside Paris. A total of 38 people were arrested.
"The opportunity will come on May 26 (the election day) when finally, the French people will be able to take back control of their future, destiny, (and) pride, which are poorly represented by a character like Macron", Salvini said in the video. "We'll be here every Saturday of the year if we have to".
"We mustn't give up", said pensioner Serge Mairesse, from Aubervilliers, just outside Paris.
Now, in their 13th consecutive week, the protests have become a sort of an uprising against the French President, Emmanuel Macron, who is seen as out of touch with common people.More news: Racism and redemption: Virginia blackface row sparks national debate
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Thousands of protesters also turned out in the French cities of Marseille and Montpellier as well as Bordeaux and Toulouse and in several cities in France's north and west.
However, the protest already went through initial phase and it is now sending a violent "knock-knock" to government's entire plans of economic reform, which in turn has been hurting the French private job growth grievously.
Interior ministry figures put the turnout across France at 51,400, of whom 4,000 marched in Paris, slightly down on the previous week's figures.
But a YouGov poll of 1,037 people issued on Thursday suggested that almost two out of three people in France (64 percent) still support the movement.
Politicians came together to condemn the arson attack on the home of Richard Ferrand, a close ally of Mr Macron, in Motreff, Brittany.