The demonstration by the Génération Identitaire organisation was banned by Paris Police Prefect Michel Delpuech, along with anti-fascist counterdemonstrations, so as to "avoid violent clashes and public order disturbances".
An appeal against the ban was turned down by a Paris court on Saturday morning.
Although they did not demonstrate, a number of the far-right group's activists were on the capital's streets on Saturday afternoon, some of them armed.
About 30 of them were stopped and searched near the Place de la République and in the south-west of the city.
About 10 descended on an anarchist bookshop near the Place de la République, chanting "France for the French!" but causing no physical damage, according to the owner.
An antifascist group that had called a counterdemonstration asked its supporters to attend one of two demonstrations - one opposing violence against women, the other slavery in Libya - in Paris on Saturday.
There was not trouble on either of those demonstrations.
Who are Génération Identitaire?
Founded in 2012, Génération Identitaire is the latest embodiment of an “identitarian” trend on the French far right.
It was born from the Bloc Indentitaire, which itself was formed after the banning of the Unité Radicale because one of its sympathisers, Maxime Brunerie, tried to assassinate then-president Jacques Chirac during the 2002 Bastille Day parade in Paris.
Having declared its opposition to anti-Semitism and anti-Zionism, it opposes “Islamic imperialism”, “anti-white racism”, multiculturalism and racial mixing, immigration and globalisation.
Its members were involved in this year’s Defend Europe operation, when they joined other European far-right groups to man a boat that aimed to prevent migrants crossing the Mediterranean to get to Europe.
Previous stunts have included the 2012 occupation of a site where a mosque was to be built on Poitiers, central France, the occupation of the headquarters of the Socialist Party to protest against then-president François Hollande’s policies in 2013, “anti-scum” patrols on public transport, and the blocking of a bridge between the “Jungle” migrants’ camp and the town of Calais.
The organisation, which claims to have 2,000 members, has organised “self-defence” training in several French towns, as well as a national training school, which attracted about 100 participants.
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