"Nothing will deter us, no threat will make France waver in the fight against terrorism," Hollande told reporters in New Delhi. "These images only serve to discredit the perpetrators of this crime."
Indian Prime Minister Narendra Modi said he had invited the French leader as a show of solidarity after the assault on the French capital, which killed 130 people and evoked memories of the even deadlier 2008 attacks on the Indian commercial capital, Mumbai.
The video purportedly shows four Belgians, three French citizens and two Iraqis said to be responsible for the Paris attacks.
They are seen carrying out atrocities, including beheading and shooting people described as hostages, in footage shot before the rampage in Paris.
There is also footage of the Paris attacks that has not been shot by IS, linking them to France's participation in air strikes against IS in Syria and Iraq.
Among the men in the video is suspected ringleader Abdelhamid Abaaoud, who was killed in a shootout with French police days after the attacks.
Brahim Abdeslam, who is the only attacker to have survived and is on the run, does not feature in it.
The jihadists, speaking in French and in Arabic, say their message is addressed to all the countries taking part in the US-led coalition responsible for the air strikes and threatens further violence against them.