"We haven't finished [with IS]," Hollande said in Erbil, which is about 60 kilometres from Mosul. "We have been told that we could attain this goal, insofar as it is possible, during the spring, in any case before summer."
Before going to Erbil, Hollande met Iraqi Prime Minister Haider al-Abadi in Baghdad.
Last week Abadi predicted that IS would be "eliminated" in Iraq in three months.
Hollande is the only head of state from the US-led anti-IS coalition to visit Iraq.
France is the second-largest contributor to the coalition's efforts, mainly through air strikes.
More than half of Mosul's eastern districts have been captured by Iraqi forces, backed by international air power, since the offensive was launched on 17 October but the west of the city is still completely under the Islamists' control.