Fabius, who will help steer the UN conference in Paris, said world leaders, supported by business chiefs and the public, were more resolved than ever to tackle climate change.
"The tone is positive, but at the same time the difficulty (of reaching an agreement) is extreme," Fabius said in an interview with news agencies in Paris on Friday.
And, he cautioned, an accord would not halt the climate juggernaut at a stroke, but instead mark "the start" of a fresh process - "a new deal."
The last time the world community tried to forge a climate pact was in 2009, at the notorious Copenhagen summit.
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The meeting was so ill-tempered and chaotic that even today, some of the wounds it inflicted on the negotiation process remain unhealed.
Fabius agreed that what he called "the Copenhagen Syndrome" was a problem, but argued there were grounds for optimism.
"The first reason for this is that, sadly, the climate situation has worsened," he said. "The need to find political agreement is even stronger than before."
Fabius also said scientific evidence had all but silenced those who contested climate change or who argued that humans were not to blame for it.
"At meetings these days, no-one challenges the reality of the phenomenon."
And, he added, there had been a dramatic change among businesses, "which are now very sensitive to the problem, and many of them have become very pro-climate."
Fabius warned though of "the extremely complex" issues that lie ahead.
If approved, the deal will be the first agreement to bring all the world's nations under the same commitment regime.
But a new round of talks, starting in Bonn on June 1, faces some massive tasks.