Jean-Yves Le Drian called the situation following a string of missile tests by Pyongyang "extremely serious" and urged the reclusive state to turn to dialogue to ease spiralling tensions.
"We see a North Korea whose objective is to have missiles capable of transporting a nuclear weapon tomorrow," Le Drian told RTL radio.
"In a few months, that will be a reality. At that moment, when it has the capability to hit the US, even Europe and at the very least Japan and China, with a nuclear weapon, the situation will be explosive."
The UN Security Council denounced Pyongyang's latest missile test, unanimously demanding a halt to its programme.
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Le Drian called on Pyongyang to "return to the path of negotiations" in a bid to ease tensions.
A joint mediation effort put forward by China and Russia would involve a mutual pause in both missile tests by North Korea as well as the joint South Korean-US military exercises by Seoul.
In July, it carried out its first two successful tests of an intercontinental-range missile, apparently bringing much of the US mainland into range.