"George Orwell said: 'Freedom is the right to tell people what they do not want to hear'," he told a news conference at city hall.
The mayor was quick to defend the work of the journalists and cartoonists who were killed during the terrorist attack.
"We have the duty to tell all the world that we will be there to protect our freedom of speech," Coderre said.
"We have the right to say what we have to say and nobody should take out that right."
Coderre also said the city continues to remain vigilant in light of recent acts that have been carried out by so-called lone-wolf terrorists.
Two separate incidents in Canada last year left two soldiers dead in attacks in Ottawa and in Saint-Jean-sur-Richelieu, Que.
Coderre, who plans to visit France in February, reminded anyone who may see suspicious behaviour on the Internet to contact authorities.
"For now, there's nothing to fear, but we are vigilant," he added.
The mayor noted 100,000 French citizens live in Montreal and that the city has close cultural, economic and political ties with France.
"That act of violence was totally unacceptable and we all felt it, so I think it's important to send a strong message that they are not alone," he said.
One longtime French resident of Montreal expressed sadness at the violence and said he and one of the shooting victims put together posters in 1968.
Jean Isseri, 73, crossed paths with cartoonist Georges Wolinski during the French student protests and described him as an "amusing" man .
"It's an extraordinarily sad event," said Isseri, a member of the board of L'Union Francaise de Montreal, which has helped integrate French immigrants since 1886.
"It's dramatic and it's a way to attack freedom of press in the name of so-called true believers in Islam."
He also expressed sympathy for the Muslim community.
"They must be extremely sad and humiliated to see that horrible attack and murder made in the name of their prophet," he said.
One late-afternoon vigil in front of Montreal city hall attracted more than 100 people, while others were planned elsewhere in the city in the evening.
Flags on municipal buildings were lowered to half-mast.