Obama Victory Brings Europe a Sense of Continuity and Relief PARIS - The victory of President Obama after a campaign that turned partly on the role of government in the American economy is likely to resonate in some unusual ways across the Atlantic, where European leaders remain locked in a contentious struggle over austerity, slow growth and the future of the European welfare state. Though European politics have their own dynamic, the role of government in a time of economic stress, which figured prominently in the campaign, is deeply divisive here as well. European experts said both President François Hollande, a pro-growth Socialist who just proposed a $25 billion cut in business taxes for France, and Prime Minister Mario Monti of Italy seemed to gain the most politically from Mr. Obama's victory. Angela Merkel, the German chancellor and the high priest of European austerity, may have more to lose. Austerity has significantly deepened Europe's slump this year, many economists say, and Ms. Merkel is facing a tougher challenge from fellow European leaders as well as her own opposition Social Democrats in Germany, who could gain from the re-election of a Democratic president in the United States who favors national health care and fiscal stimulus. For the British prime minister, David Cameron, who championed austerity, the re-election of Mr. Obama may deprive him of an economic soul mate, but it also leaves in place a firm ally on issues of free trade and security. The impact of Mr. Obama's re-election may be limited to a degree by his faded appeal around the Continent compared with 2008, when he was hailed as a hero. "This is a president whose policies are closer to European policies," said Laurence Nardon, head of the United States program at the French Institute for International Relations. The French adore Obama but in a strange way, because he is not very warm and he hasn't truly clicked with European countries. He is seen as generally supportive of European efforts to deal more firmly and quickly with the euro crisis, sending Treasury Secretary Timothy F. Geithner to hector European leaders to act fast and not rely only on austerity measures to deal with fiscal debt. For a time, Mr. Geithner's name was reviled by some Europeans, especially Germans, as someone handing out advice while letting the American debt balloon far beyond European levels. There was greater appreciation in Italy from supporters of Mr. Monti, who found a quiet ally in Mr. Obama against the austerity dogma of Germany. "I think Mario Monti found a good talking partner in Obama," said Sergio Romano, a columnist for the daily newspaper Corriere della Sera and a former ambassador. Even if Obama is not particularly involved in European issues, the resolution of E.U. woes has been essential to his economic policy, and Monti offered him a guarantee that Italy was acting. On the other hand, Monti needed to restore Italy's political, economic and financial credibility at the international level, and Obama offered him a chance to do so. Mr. Hollande summed up the hopes of the European left neatly in his official congratulations to Mr. Obama, which he sent to "Cher Barack." "Your re-election is a clear choice in favor of an America that is open, united, fully engaged on the international scene and conscious of our planet's challenges: peace, the economy and the environment," Mr. Hollande said. He added that he hoped the election result would bring a renewed focus on "economic growth to battle against unemployment in our countries." Volker Perthes, director of the German Institute for International and Security Affairs in Berlin, said Ms. Merkel, who is up for re-election this year, ultimately has a decent working relationship with Mr. Obama, despite their clear differences. "Merkel and Obama embrace very different economic philosophies," Mr. Perthes said. She doesn't much like Keynesianism and quantitative easing. But it's easier for them to work with the people they know. In any case, the German model of social market capitalism that Ms. Merkel favors remains left-wing in American terms, reliant on a large state welfare system and national health care. "There would not have been much fun between Merkel and Paul Ryan," Mr. Perthes said. Maïa de la Baume and Scott Sayare contributed reporting from Paris, and Gaia Pianigiani from Rome.