The interior minister, Manuel Valls, said a fight broke out on Wednesday evening between two groups of young people in a street just steps away from the famous Printemps department store in Paris.
Clement Meric, a 19-year-old student at Sciences Po, one of France's most prestigious universities, was beaten by several skinheads, according to Valls.
No suspects have been arrested, and Valls told reporters at the scene of the attack – a crowded, pedestrianised area with cafes and chain stores – that finding them is the top priority.
It was unclear how the fight developed and how many people were involved.
Political tensions are high in France after months of protests against legalising gay marriage, that sometimes ended with troublemakers from the extreme right clashing with police.
Gay rights organisations have also warned that gay people were being targeted before the Socialist government's "marriage for all" bill was passed.
Politicians from left and right lashed out at the violence, as did Valls, who focused his anger at the skinheads.
"There is no place for small neo-Nazi groups whose enemy is the nation. A group of the extreme right is at the heart of this assassination. There is a discourse of hate and a climate that favours this discourse. We need to pay attention to this because they threaten our values."
The Party of the Left said Meric, one of its activists, was declared braindead. The party, one of several small political movements on France's vocal and active far-left, called for demonstrations in Paris against violence by groups on the extreme right.