The motive for the attack was not clear but incident did not appear to be terrorism-related.
According to media reports, three people were taken hostage, including a pregnant woman.
The hostages are being held in the internal courtyard of the building, which contains a mix of offices and residential apartments. The information could not be officially confirmed.
Anti-terrorist police are surrounding the Mixicom computer store in the French capital's 10th arrondissement, close to the Gare du Nord Eurostar hub. However, his motivation for such an encounter was unknown.
French Open 2018: Rafael Nadal admits to nerves after Diego Schwartzman scare
He is the only man to beat the world number one on clay in the last two years - in Madrid this spring and in Rome last year. And on the penultimate point of the semifinal, after being run ragged, the 2009 US Open victor could only offer up a smile.
Witnesses said the man claimed to be in possession of a gun and bomb.
An armed police officer and a sniffer dog search the area.
Police would not immediately confirm whether the person holding the hostages was armed or describe the nature of his demands.
Negotiations with the suspect were taking place, according to an Interior Ministry official who couldn't be identified because the operation was in progress.