Bonjour, Hollande. Ready for a gentle arm-twisting at the White House?

President Obama invites the new French president, François Hollande, to the White House Friday morning at some political peril.

After all, certain reaches of the blogosphere and cable talk shows may well trumpet the news that Europe’s latest openly Socialist leader is being feted (in the American people’s house!) by the world’s most powerful closeted socialist.

Though it may be true that the two leaders, broadly speaking, fall on the growth side of the growth-versus-austerity spectrum for addressing the eurozone’s economic ills, that doesn’t mean the tete-à-tete will be a love fest.

For one thing, the American president remains “cool Obama.” Unlike his predecessor, George W. Bush, who professed to seeing into Vladimir Putin’s soul and who playfully (and oh-so awkwardly, as it turned out) massaged one of Angela Merkel’s shoulders in public, Mr. Obama doesn’t easily warm to other leaders.

But there are other reasons for some trepidation on the American president’s part. One is Afghanistan.

Remember when Obama warned in March against any “rush to the exits” in the form of a precipitous withdrawal from Afghanistan? He was speaking after a string of terrible incidents involving US soldiers that led some critics (and a growing majority of Americans) to call for a swift conclusion to the US war effort.

But he might have been speaking to then-candidate and now-President Hollande.

One of Hollande’s few foreign-policy pledges in his campaign to dethrone Nicolas Sarkozy was to remove all French combat forces from Afghanistan by the end of this year. He made that commitment despite NATO’s policy, adopted at its summit in Lisbon in 2010, to have all international security forces transition out of a combat role by the end of 2014.

Still, Obama is unlikely to bluntly tell the new French leader that his lights-out date is two years too soon. More probable is a friendly reminder of the alliance’s “in together, out together” slogan for the Afghan campaign, and a query as to what tasks the French plan to maintain in Afghanistan – to 2014 and beyond.

Obama's aides gave some hints at a briefing with reporters Thursday on how the president will approach Hollande on Afghanistan. The president understands the importance of campaign commitments, said National Security Adviser Thomas Donilon, adding that has to be weighed against the fact that France is a member of the alliance.

“We’ll have a discussion with the French on where they want to go on this,” said Mr. Donilon, noting that NATO’s “framework” for the Afghan transition “allows for different kinds of contributions.”

At its summit in Chicago this weekend, NATO is expected to adopt a new goal of shifting command of combat operations over the next year to the Afghans anyway, so perhaps what Obama hopes to hear from Hollande is the commitment the French president is willing to make to a training program for Afghan security forces.

The two leaders might be expected to be more in sync on the economy, given that Obama has pressed his European colleagues for more growth and job-creating measures since taking office, and given that the Socialist Hollande campaigned on a promise to soften European austerity.

But Obama can hardly afford to emerge on the White House balcony, arms linked with Hollande, to declare an entente on stimulus measures. Sure, there’s the scarlet S (for socialist) he wants to avoid, but there’s something else.

Obama will gather the leaders of the Group of Eight (G8) developed countries at Camp David Friday evening. The champion of European austerity, Germany’s Angela Merkel, will be there, so it would not be proper etiquette for the US president to play favorites and show a preference for one leader’s approach over another’s.

As Donilon says, Obama’s job at the head of the Camp David dinner table will be to hear from everybody, not stoke the differences. “Let’s let the leaders speak for themselves,” he says. “As host, the president will lead the discussion.”