France’s government, led by President François Hollande, has emphasized giving the most vulnerable members of the euro area leeway when making painful economic adjustments. By contrast, the Netherlands, along with Germany and Finland, has pressed indebted nations like Greece and Portugal to tighten their belts despite the recessionary effect on their economies.

One factor that could help the French swing in support of Mr. Dijsselbloem, a member of the Dutch Labor Party, is that he, like Mr. Hollande, is a socialist.

Regarding the soon-to-be created single banking supervisory agency for the euro zone, Mr. Juncker suggested on Thursday that a Frenchwoman could be offered a senior role. And although Mr. Juncker again did not offer names, there are reports in the French news media that Danièle Nouy, an official at the Banque de France, could be offered such a role, partly to assuage French concerns.

Mr. Dijsselbloem, 46, won the finance portfolio, his first Netherlands cabinet post, late last year, and he has little experience at the top levels of government or in European affairs. But he did take office in time to participate in a round of marathon meetings by finance ministers to forge agreements on resuming aid to Greece and the creation of the single banking supervisor.

“I suppose he is suitable, as he wouldn’t be finance minister,” said Sophie in ’t Veld, a Dutch member of the European Parliament for the Democrats 66, a liberal and pro-European political party.

“But how,” she asked, “is he going to navigate between the deeply euro-skeptic electorate and a deeply euro-skeptic Parliament that will expect him to be a troublemaker in Europe and, on the other hand, show compromise and consensus as the head of the Eurogroup?”

Mr. Dijsselbloem told the Dutch daily newspaper De Volkskrant at the end of December that he regarded “strengthening European cooperation inevitable and good for the Netherlands.” But he also cautioned that, “when it comes to Greece, for example, everyone looks to the Netherlands, and we have to take the floor” and that, “from us, from Germany and Finland, it’s expected that we exhibit some strictness.”