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.