Piotr Pavlensky, who is best known for nailing his scrotum to the ground on Moscow's Red Square in 2013, was arrested along with his partner, Oksana Chaligui, at 4.00am on Monday.
They were standing in front of the bank as flames licked parts of the facade.
Pavlenski in front of the Banque de France agency
In a statement he linked his action to the destruction of the Bastille prison during the French revolution, claiming that "bankers have taken the place of monarchs" and calling for the "rebirth of revolutionary France" to "set off the worldwide blaze of revolutions".
Pavlensky sets fire to the Banque de France agency on Place de la Bastille
On Tuesday morning he was admitted to a police psychiatric unit but on Wednesday the couple were charged with "destruction of property in a fashion dangerous to persons" and placed in pretrial detention.
According to his lawyer, Dominique Beyreuther Minkov, Pavlensky has started a hunger strike to protest the lack of "public debate" when he appeared before the magistrate.
As well as the Red Square performance - a demonstration against Russian state power - the 33-year-old artist has sown his lips together in protest at the jailing of feminist punk band Pussy Riot, wrapped himself in barbed wire and chopped off part of his ear.
In November 2015 he set fire to the doors of the headquarters of Russia's secret police, the FSB, for which he was found guilty of damaging a cultural site and fined 500,000 rubles (7,400 euros).
Pavlensky spent a month last year in a notorious Russian psychiatric hospital undergoing state-ordered tests that found him sound of mind.
He was granted political asylum in France after being accused of sexual assault by an actress - a charge he inisists is false and politically motivated.