The building, where King Charles III is set to be received next week, was set on fire Thursday evening.
Unrest over pension reform in France grew on Thursday, with Bordeaux town hall set ablaze.
More than a million protesters took to the streets across France, amid renewed violence and tension.
457 arrests were made and 441 police injured, according to the country's Interior Minister Gérald Darmanin.
The porch of the Bordeaux town hall, where King Charles III is set to be received early next week, was set on fire Thursday evening. It was not clear who is behind the blaze, which firefighters quickly extinguished.
Unrest - now in its ninth day - was sparked by French President Emmanuel Macron's attempt to increase the retirement age from 62 to 64.
He claims the reform is necessary to make the system economically viable, with increasing numbers of pensioners putting a burden on the state.
However, it is deeply unpopular and Macron's use of special powers to force the legislation through parliament has been sharply criticised as anti-democratic and authoritarian.
Polls suggest up to 70% of French citizens reject the reform.
France's powerful unions have spearheaded the protest movement, with one in six civil servants on strike yesterday, while tons of rubbish is piling up on the streets amid industrial action by refuse collectors.
Between 1 and 3.5 million people are believed to have marched in 300 cities yesterday.
Violent clashes between riot officers and protesters have punctuated several protests in recent days, with Prime Minister Elisabeth Borne deeming the "violence and degradation" "unacceptable".
The police, in turn, have been accused of using excessive force. Footage circulating online purports to show a group of riot officers pointing a firearm at the press covering one protest.
The fire in Bordeaux lasted around fifteen minutes and damaged the massive wooden door of the building, before being extinguished by the firefighters, according to Pierre Hurmic, mayor of Bordeaux.
"It's the house of Bordeaux, I don't really see the symbol behind it," he said, adding he was "very shocked".
Investigations are in progress.
Unions have called for further protests next Tuesday, which would coincide with King Charles III's state visit to the country. He is scheduled to visit the southwest city of Bordeaux that day.
For the first time since the start of the protest, tear gas was fired by the police at groups of masked young people throwing projectiles and setting fires at barricades in Bordeaux.
Thursday's demonstration in the wine-producing city brought together between 18,000 and 110,000 people.
Meanwhile, seven people were arrested for throwing projectiles, arson and contempt, according to the authorities.
Violent clashes were reported in Nantes and Rennes, where water canons were used, plus a police station in Lorient was targeted. Lille and Dijon were also reportedly tense.
In Brest, Aurélia Vaillant, a 44-year-old restaurateur, told AFP she "will go all the way".
"There is too much at stake to stop now", she said, adding that Macron was "despised" for using constitutional powers to force the legislation through without a parliamentary vote.
On Wednesday, Macron remained resolute, maintaining his reform was "necessary" while describing the perpetrators of violence as "factious".