- NEW: President Obama invites France's new president to the White House
- Results of French and Greek elections have implications for U.S. economy
- France's president-elect says he plans to pull troops out of Afghanistan this year
- Sarkozy was one of the most America-friendly French presidents in decades
(CNN) -- The U.S. economy is currently on autopilot: A sharply polarized Congress and a tapped out Federal Reserve can't do much more to stimulate it this year.
But the economy may still hit turbulence after voters in France and Greece delivered a resounding anti-austerity message over the weekend to their governments.
That message, say analysts, is likely to have implications for the United States that extend from its fragile economy to its planned withdrawal from Afghanistan.
The first sign of a possible issue could come as early as Monday when U.S. markets open.
"A change in leadership brings uncertainty because you don't know exactly what you're getting into," said Ryan Detrick, senior technical strategist at Schaeffer's Investment Research.
"It won't be a be-all end-all sell signal, but new leadership in France could cause investor jitters that reverberate through global financial markets."
Even the news Friday that Nicolas Sarkozy, one of the most America-friendly French presidents in decades, may lose to socialist Francois Hollande appeared to play a role in the market's movement. After nearing four-year highs at the start of the week, U.S. stocks ended with a thud on Friday as the S&P 500 logged its biggest weekly decline of the year.
Hollande swept to victory Sunday, becoming France's first-left wing president since Francois Mitterand left office in 1995.
That was followed by news that voters in Greece dealt major blows to the country's two most established parties in parliamentary elections, leaving no party with anything approaching a majority.
The message from voters in both countries appeared to be the same: The current policy of deficit-cutting, reduced spending and cuts to benefits and public services is unacceptable.
The election results leave in question what happens now to the eurozone and its debt crisis. France is a key player in plans to navigate it. And Greece is a recipient of bailout by the European Central Bank that requires the government to slash spending.
The European Union is America's largest trading partner. The U.S. economy has suffered in the slow down in European markets, and further economic problems in the eurozone could mean less trade with the United States.
Outside of the economy, the election of Hollande poses serious questions about the diplomatic and military relationship between the United States and France.
With Sarkozy, the United States enjoyed support in its positions on Syria, Iran and Afghanistan. Sarkozy was a proponent of the NATO air campaign in Libya.
But with Hollande, there is no guarantee that the United States can count on support.
Hollande campaigned on the promise to pull France's troops from Afghanistan by the end of the year, two years ahead of a planned withdrawal that was choreographed to coincide with U.S. plans.
During the campaign, Hollande also raised questions about Sarkozy's decision in 2009 to place French troops under NATO command.
Hollande can expect NATO leaders to urge him to change or soften his position when he attends a summit in Chicago later this month where the focus will be on Afghanistan.
President Barack Obama called Hollande shortly after results were announced to congratulate the president-elect and invite him to the White House.
While any talks between the two leaders will likely to focus on diplomatic and economic relations, Obama is probably taking a lesson from the outcome of the French election.
Obama, like Sarkozy, is campaigning for re-election amid a faltering economy, high unemployment and voter discontent over spending and cuts.
CNN's Hibah Yousuf, Alan Silverleib and Chelsea J. Carter contributed to this report.
