Unconfirmed reports said Abdelhamid Abaaoud, the alleged mastermind of the attacks, is the focus of the operation.
The so-called Islamic State (IS) group has said it carried out the attacks in which 129 people died.
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Roads have been blocked off around Rue de la Republique in Saint Denis, in the same district as the Stade de France, where suicide attackers detonated bombs on Friday.
Radio Monte Carlo reporters at the scene said more than one suspect had been cornered in a block of flats.
Amateur video aired by TV stations BFMTV and iTele cited witnesses saying sporadic gunfire had rung out since around 04:30 local time (03:30 GMT).
Deputy Mayor Stephane Peu urged local residents to stay indoors, saying "it is not a new attack but a police intervention".
The deadly attacks have put European countries on high alert. On Tuesday evening, a football friendly between Germany and the Netherlands was cancelled shortly before kick-off and the stadium in Hanover evacuated after "concrete" information about a bomb threat, according to the city`s police chief.
Part of Hannover railway station was also closed while a suspicious object was investigated.
Meanwhile, two Air France planes heading to Paris from the US were diverted because of security threats. One was sent to Halifax in Canada, the other flew to Salt Lake City in the US state of Utah. Both planes landed safely and the passengers were unharmed.
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