The battles to retake Raqa in Syria and Mosul in Iraq are expected to be the most difficult of the war against IS, which holds swathes of territory in both countries.
Le Drian's remarks are the most specific timetable for the cities' recapture given by a member of the US-led coalition against the jihadists, which has been reluctant to comment on the expected pace of operations.
"Raqa and Mosul must fall in 2016," Le Drian said, calling for making it "the year of a major turning point in our struggle against the so-called Islamic State".
IS claimed attacks in Paris that killed 130 people in November last year, and there is concern that the jihadists will strike the country again.
Belgium's federal prosecutor has said a jihadist cell that attacked Brussels airport and a metro station last month, killing 32 people, initially planned to target France.
Raqa was seized by the jihadists in early 2014, and Mosul was overrun during an IS offensive in June that year.
The fact that both cities still have large civilian populations will complicate efforts to retake them, and the jihadists have had ample time to sow slews of bombs and set up other defences.
Lieutenant General Sean MacFarland, the commander of the international operation against IS, has said that Iraqi generals do not think they will be able to recapture Mosul until the end of 2016 or early 2017 at the earliest.
This year "must be the year of the beginning of the end for Daesh", Le Drian said in his speech to Iraqi special forces and French troops, using an Arabic acronym for IS.
But he cautioned that despite having suffered a string of defeats, the jihadists are still a threat.
'More dangerous than ever'
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"Because it's cornered, Daesh is more dangerous than ever," he said.
IS is still able to carry out frequent bombings in government-held areas, as well as mount raids targeting security forces.
Le Drian arrived in Baghdad on Monday for talks on the war against the jihadists, meeting with Prime Minister Haider al-Abadi, President Fuad Masum, parliament speaker Salim al-Juburi and Defence Minister Khaled al-Obeidi.
According to the French military, France has carried out more than 580 strikes against IS, destroying over 1,000 targets, and has around 350 soldiers deployed to Iraq.
Le Drian, who arrived in Baghdad from Kuwait, has already visited some of those troops.
The United States carries out the majority of coalition strikes and has deployed some 3,900 military personnel to the country, including special forces targeting IS with raids.
The jihadist group overran large areas north and west of Baghdad in June 2014, but Iraqi forces have since recaptured significant ground with backing from the coalition, while Syrian forces have also made gains against IS.
Le Drian's visit comes just days after US Secretary of State John Kerry vowed during a trip to Baghdad that the coalition and Iraq would turn up the heat on IS.
In addition to major security challenges, Iraq has also been hit by an economic crisis caused by slumping oil prices, and political tensions over efforts to replace the current cabinet.
Abadi has called for "fundamental" change to the cabinet so that it includes "professional and technocratic figures and academics", and presented a list of nominees to parliament last week.
But powerful Iraqi parties and politicians rely on control of ministries for patronage and funds, and lawmakers said the political blocs are nominating other candidates.
Officials have said a vote on new candidates could take place on Tuesday, but the end result may be a variation on the current system of party-affiliated ministers.