Mulcair, leader of the Opposition, holds dual French and Canadian citizenship. But given his current job, he did not vote in Sunday's presidential election.
"I simply send along my warmest greetings and my hearty congratulations to Francois Hollande for an extraordinary victory," Mulcair said Monday.
"I think that his policies are going to prove most interesting in the years to come."
Hollande, a Socialist, officially becomes France's new president on May 15.
He narrowly defeated President Nicolas Sarkozy — the latest victim of a wave of voter anger over spending cuts in Europe that has ousted governments and leaders in the past couple of years.
Mulcair was careful with his comments, saying that Hollande's presence in Europe could help resolve financial issues. He called the incoming president's approach a "balanced" one and said he knew many members of Hollande's team.
"I think that Mr. Hollande is a very experienced politician who has been elected many times and served his country well," Mulcair said.
"That wealth of experience ... is the type of thing that will allow us to put in place policies that will stabilize the situation in Europe."
Mulcair, who is not the first politician to hold dual citizenship, has said he is proud to hold both Canadian and French citizenship.
The issue of dual citizenship has generated controversy in the past with former Liberal leader Stephane Dion and with Michaelle Jean, who gave up her French citizenship to become governor general.