Pyotr Pavlensky, 34, received a one-year jail term and two years suspended for the stunt, but should walk free, having already served 11 months in custody.
His former partner, Oksana Shalygina, received a two-year sentence, 16 months of which were suspended.
But Pavlensky was also ordered to pay 21,678 euros ($25,000) in damages to the Banque de France. "Never!" he said in Russian.
Pavlensky fled to France and was given asylum in 2017 after several provocative protests drew the ire of Russian authorities, not least one in which he nailed his scrotum to Moscow's Red Square.
In France, Pavlensky kept up his work. In October 2017 he and Oksana Shalygina torched the front door of the Paris Bastille branch of the Banque de France.
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Locating it on the Place de la Bastille, where the French Revolution began in 1789, was "historically shameful", he argued, adding: "Bankers have taken the place of monarchs."
They were convicted of "dangerous destruction of property".
Shalygina had been freed ahead of trial in January 2018, but the court at first deemed Pavlensky a flight risk and ordered him held in custody. He was eventually released last September.
After making global headlines with his Red Square scrotum performance titled "Fixation" in 2013.
2016, a Russian court fined him after he doused the doors of Russia's FSB secret police headquarters with petrol and set them on fire.
Pavlensky has also sewn his lips together to protest the jailing of members of the feminist Russian punk group Pussy Riot, wrapped himself in barbed wire, and chopped off part of his ear.
In December 2016, Russian authorities said a theatre actress had accused Pavlensky of sexual assault, charges he denounced as fabricated.
He says he risks 10 years in a prison camp if returned to Russia.
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