France's (as well as Greece and a few other European countries) economy directly ties to our economy as the one true Global Economy is in full swing, unbeknownst to many Americans. Aside from some key examples such as North Korea and even recently, Cuba, trade is free or aceessible nowadays.
To put things in context, the United States economy has improved over the last 8 years while the Greek economy has nearly defaulted. A single country in the European Union would not likely create a significant economic issue for the United States. The EU should be able to handle small issues within their own collective economy. If there was a larger systemic crisis that took the entire EU into a crisis, it would impact the US.
I think that the French economy can never be compared to the United States economy, and I highly doubt an improvement in the French economy would affect or threaten America. Having said that, I do believe that when the world economy is healthy, it benefits most, if not all, nations. So I do hope that France continues to emerge economically.
The economic emergency in France is primarily based around the country's massive unemployment problem, particularly among its young people. France is making an effort to create vocational training opportunities to address the unemployment crisis. This is obviously a difficult situation for France, however it should not have an impact on the economy of the United States.