Two gunmen are said to be still at large.
Reports say up to 40 shots were fired outside the venue in the Danish capital.
Controversial Swedish cartoonist Lars Vilks, who in 2007 drew pictures of the Prophet Muhammad dressed as a dog, was also present at the debate.
Shortly after the attack, a message appeared on the Twitter feed of French ambassador Francois Zimeray saying he was unharmed.
The area around the venue, reportedly a cafe, is under lockdown, the BBC's Malcolm Brabant reports.
Police have erected cordons and are searching a nearby park, he adds.
One dead and three injured in Copenhagen 'terrorist attack' in The Guardian.
Copenhagen shootings: Police kill 'gunman' after two attacks from BBC News.
The attacker was named Omar El-Hussein, a 22-year-old native Dane who was previously wanted over a train stabbing.