PARIS — It took almost two weeks for negotiators from 195 countries to finally pass the landmark climate accord this weekend after several espresso-fueled all-nighters and long, passionate debates over the meaning of a single word, such as “shall”.

But the story of how the deal came together started long before that — in December 2009, with the failure of the last such summit meeting, in Copenhagen.

That gathering was, in hindsight, a case study in how not to do a deal. The hosts of the event had set a stern tone, with concrete barricades, concertina wire, and steel cages to house protesters who stepped out of line.

Connie Hedegaard, Denmark’s minister of climate and energy, was blunt in her approach, “putting pressure on all governments to make the political price of being an obstacle so high that no one will pay it,” she said at the time.

In the tense final hours, world leaders from a handful of large countries took the negotiations into their own hands, leaving smaller countries fuming. Little emerged from the talks, other than acrimony and suggestions that perhaps such summit meetings were ultimately futile. “After Copenhagen, many world leaders believed that the United Nations process would no longer work for tackling climate change,” Secretary General Ban Ki-moon of the United Nations said in an interview. “It was deeply disappointing. It was painful.”

So what changed from Copenhagen to Paris? In short, three things: a fundamental change in the geopolitics of climate change; a shift in the perception of global warming from a distant warning to an immediate threat; and the art of French diplomacy during the event and in the months beforehand to soften the sharp elbows of negotiators and reduce the chances that major points of contention might kill a deal again. In particular, they made sure that each country, regardless of its size or wealth, felt its voice would be heard.

“It was a wonderful surprise that after the incredible disappointment of Copenhagen, these 195 countries could come to an agreement more ambitious than anyone imagined,” said Jim Yong Kim, the World Bank president, who has been closely engaged in the talks. “This never happens.”

The talks in Copenhagen were handicapped before they even began, as major countries viewed President Obama with deep skepticism. The reputation of the United States on climate change had suffered because of its decision, under President George W. Bush, to withdraw from the world’s first climate treaty, the Kyoto Protocol.

Americans had historically demanded action from other nations while doing little at home, despite the country’s status as the world’s largest greenhouse-gas polluter through recent decades. And the United States was locked in an impasse with China, the world’s other largest polluter, as each country waited for commitments from the other before acting itself.

Mr. Obama, still early in his first term and having just won the 2009 Nobel Peace Prize, promised other world leaders in Copenhagen that all this would change under his administration. He assured them that Congress was on the verge of passing a sweeping new climate change bill, sponsored by Senator John Kerry of Massachusetts.

But Mr. Obama’s pledges won him little credibility. He was treated dismissively by the Chinese premier, Wen Jiabao, who sent him progressively lower-level officials for the final negotiations. In the strained closing hours of the conference, Mr. Obama burst into a meeting with Mr. Wen and other leaders, where they worked all night on laptops to hammer out the terms.

Ms. Hedegaard had signaled a few months before the talks began that failure was not an option for the deal. “China and other emerging nations must accept it even if it isn’t fair,” she said.

But force of will would not carry the day, and the late back-room deal failed to win the consensus required for a legally binding agreement, as a handful of countries, including Venezuela, Bolivia and Cuba, blocked its passage. “The rich are destroying the planet,” said Hugo Chávez, the Socialist president of Venezuela, during the talks. “Perhaps they think they’re going off to another one after they’ve destroyed this one.”

Soon after Mr. Obama returned home, Mr. Kerry’s climate change bill failed in the Senate. And for the rest of his first term, Mr. Obama put the issue of climate change on the back burner.

That changed after his re-election. Even Mr. Obama’s own aides were surprised when he told them in early 2013 that he intended to put climate change at the heart of his second term. In his first State of the Union address after his re-election he warned Republicans on climate change, saying, “If Congress doesn’t act, I will.”