The government is also working on ways to put the onus on "the troublemakers, and not taxpayers" to pay for damage to businesses and properties.
On Saturday, demonstrators used a construction site vehicle to smash open the doors of a government building.
The former heavyweight boxer had been sought by the authorities after video emerged of him hitting a police officer while other protestors aim kicks at the policeman.
The "yellow vest" campaign is said to be the biggest political crisis of Macron's 20-month presidency and has brought his popularity ratings to an all-time low.
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Mr Dettinger, known in the ring as "The Gypsy From Massy", a town near Paris, gave himself up to the police in the capital on Monday.
Christophe Dettinger handed himself to police and was immediately detained.
The "yellow vest" movement mobilized through social media has forced Macron to reconsider his economic and social recipe for the eurozone's No.2 power by offering a series of concessions to appease angry citizens.
Recent surveys suggest 75 per cent of the public oppose his government's policies and 60 per cent were unimpressed by his New Year message, in which he said he understood popular anger but remained committed to his reform programme.
Disturbing footage emerged showing police beating protesters in the southern city of Toulon, with multiple media reporting that the incident is now under investigation for brutality.
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Like in Italy, where the rather populist left-wing movement formed an alliance with the far-right to govern, the "yellow vests" movement attracts both the far-left, which unreservedly supports them, and the far-right, which has had a strong presence in violent demonstrations.
Since November, demonstrations initially triggered by a tax hike on diesel fuel and expanded to encompass the high cost of living have led to violent clashes with police in Paris and other cities - including most recently on Saturday.
Di Maio applauded the yellow vest's interest in direct democracy, offering to provide the yellow vests with some of the online tools the Movement employs to organize grassroots events on a local level and to choose its representatives - despite the yellow vests' lack of formal spokespeople.
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Deputy Prime Minister Luigi Di Maio, head of the anti-establishment Five Star Movement (M5S), wrote on his party's blog Monday: "Yellow vests, do not weaken!"