"It was the same targets that were chosen by the terrorists", said Hollande, speaking on a visit to the Danish embassy in Paris.
"We see there is a link that doesn't show there is a network but does show the terrorists are determined to hit what we are, what we represent, the values of freedom, of law, of protection that every citizen -- whatever his or her religion -- should have," the president added.
Denmark and France are both countries in mourning but with the "same desire to resist and to overcome terrorism," vowed Hollande, as he expressed his country's "solidarity" with Copenhagen.
Several parallels have been drawn between the Copenhagen attack and the killings in Paris in January, with the gunmen in both cases targeting symbols of freedom of speech, police and Jews.
Danish authorities have warned that the man suspected of carrying out the twin killings in Denmark "may have been inspired by the events that took place in Paris" between January 7 and 9.
French ambassador to Denmark Francois Zimeray, who had been present at the debate but was not hurt, told AFP the shooting was an attempt to replicate the January 7 attack against the Charlie Hebdo weekly in Paris, which left 12 people dead.
"They shot from the outside (and) had the same intention as Charlie Hebdo, only they didn't manage to get in," he said by telephone from the venue.
"Intuitively I would say there were at least 50 gunshots, and the police here are saying 200," he told AFP.
"Bullets went through the doors and everyone threw themselves to the floor."
French Foreign Minister Laurent Fabius condemned what he called a "terrorist attack targeting a public meeting", saying in a statement that France "remains by the side of the Danish authorities and people in the fight against terrorism."