Usually, American shareholders don't have to worry much about the French presidential election. It rarely has any implications on the stock market in the U.S., especially in the short term.
This time, however, it is different.
The central issue lies in the lingering shadows of the debt crisis in Europe, which over the past year has been centering around Greece. Spain, Portugal, and Italy were also to some extent in trouble. Prior to the election in France, the crisis has reached an awkward equilibrium, with the whole Eurozone bending towards the demand of its strongest economy, Germany. Germans are very conservative financially, which is a good thing generally. It is one of the reasons why Germany is not having any direct trouble this time.
However, in resolving the financial crisis, Germany has been insisting on countries taking EU help to get onto austerity programs. The logic seems impeccable: since too much public debt is the root of the problem, let the governments cut spending in order to balance budget and curb debt. However, at the time of a deflationary driven financial crisis, this is not exactly the right direction to solve the problems quickly. Anyway, that's a long story for another day. The European debt crisis is currently under control based on austerity dominated programs throughout different countries.
The election in France may change that. Socialist Francois Hollande was elected as the new president, replacing Nicolas Sarkozy. On the political map of France, Sarkozy is on the right. Hollande is further on the left. This means Hollande is likely going to prefer a more Keynesian type of government spending driven solution out of the crisis than to only shrink debts through spending cuts. It wouldn't be a problem if France was still using the Franc as its currency - it is not.
As part of Euro zone, France cannot act alone by simply printing money to inflate itself out of the crisis. Now that Hollande is the president, it is possible that France will have a different stance on resolving the current financial crisis. If, as the two biggest economies in Eurozone, Germany and France start to have disagreements on how to proceed, the financial crisis can come back again quickly. At the very least, it will create a big uncertainty in the currently delicate equilibrium in Europe.
Is that going to happen? Well, it doesn't have to happen to create chaos in the market - as long as the market smells uncertainty. In this case, the expectation of resolution among Eurozone mega countries themselves will lead to a big drop in the stock market, which would almost certainly make banks more likely to conserve cash and less likely to lend. By itself, the expectation could become a self fulfilling prophecy and create a financial crisis.
I expect high volatility in the market before Hollande's stance is fully known. In the meantime, as it often happens during the past year, when a crisis siren starts, the dollar rises, and the stock market falls.