The man equipped with a military weapon took an unconfirmed number of hostages at the post office in the town of Colombes, just outside the capital.
"I cannot confirm or deny whether it is linked to terrorism," an official at the city prosecutor's office told Reuters earlier, declining to give further details.
BFM TV, citing an unidentified source, said the hostage drama was not related to last week's attacks in Paris.
French police arrested 12 people earlier on Friday suspected of helping militant Islamist gunmen in last week's killings in Paris. There have been numerous false alerts across the city since the attacks.

Meanwhile, a photographer with French news agency was wounded in Pakistan on Friday after being shot during clashes against the satirical weekly Charlie Hebdo outside the French consulate in the port city of Karachi, police said.
"AFP photographer Asif Hasan suffered wounds resulting from gunshots fired by ... protesters, police have not opened fire," Abdul Khalique Shaikh, a senior police officer in southern Karachi, said.
A photographer at the scene said that many protesters appeared to be armed.
Pakistan police fired tear gas and water cannon at about 200 protestors outside the French consulate in the southern port city of Karachi when a demonstration turned violent.
It was the first time people's anger over the cartoons lampooning Islam's Prophet Mohammad spilled into violence in deeply conservative Pakistan.
Last week, 17 people were killed in France in three days of violence that began with a shooting attack on Charlie Hebdo, known for its satirical attacks on Islam and other religions.
Charlie Hebdo's first edition since the attack, published on Wednesday, featured a cartoon of the Prophet Mohammad on a cover that defenders praised as art but critics saw as a new provocation.
In Karachi, mostly students gathered outside the consulate on Friday afternoon shouting slogans, and the standoff quickly turned violent. Police had sealed of several streets leading to the area.
A reporter aid some of the protesters appeared armed with guns and he saw them firing shots after security forces used water cannon and tear gas to stop the crowd advancing on the consulate.
A photographer with French news agency was wounded the clashes, police said.
At least three people were wounded and taken to hospital, one in critical condition, a Karachi doctor said.

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