Quentin Deranque died after suffering brain damage when he was attacked by at least six people during a protest by the French far-right in Lyon.
The demonstration was directed at a left-wing politician who was giving a speech at a university in the city.
The fatal assault has intensified tensions between the far-right and the far-left.
One of those arrested is said to be an assistant to MP Raphaël Arnault from the left-wing party Indomitable France (LFI); the person targeted has been banned from accessing the National Assembly.
LFI party leader Jean-Luc Mélenchon condemns the assault.
