Maverick left-winger Montebourg is the third former minister from President Francois Hollande's Socialist government to declare his intention to stand as a candidate after former ecology minister Cecile Duflot and Benoit Hamon, who once headed the education ministry.
“I am a candidate because it is impossible for me to support Francois Hollande,” Montebourg told supporters in Burgundy.
“The results of his five-year term are simply indefensible,” Montebourg added, highlighting a still fragile economy and a rebellion by some lawmakers against Hollande's efforts to beef up national security in the wake of jihadist attacks that have killed more than 200 people in the last two years.
He called on Hollande to “think long and hard” about whether to stand for re-election. Montebourg, who left the government in 2014 as his criticism of Hollande grew louder, proposed re-introducing national service as France contends with the constant threat of attack.
A supporter of protectionism to safeguard the French economy, Montebourg also said that as president he would pull France out of EU treaties that did not serve its interests.
Hollande, whose approval ratings are the lowest of any French president in modern times, has said he will announce before the end of the year whether he will run again. Polls show he could still win the Socialist primary in January, which appears to be tailor-made for the unpopular president to re-assert his authority.
Duflot launched her bid Saturday in a letter to left-wing newspaper Liberation in which she conceded that the ecologists had “little space” in a race expected to be a three-way between the candidate of the right-wing Republicans, the Socialist candidate and the far-right National Front leader Marine Le Pen.
Former president Nicolas Sarkozy is expected to throw his hat into the ring as the Republicans' candidate in the next few days.