Unfortunately, there is no real free market in this world. Since the most central and liquid asset in the world, the dollar, is controlled by state power, nothing else can escape the fact that all supply and demand is indirectly driven by policies of the US government and the Fed.
In general, the US wants exchange rates to float, but most other governments want them to be more-or-less 'stable.' This is because the dollar serves the same role as gold in the past. Governments generally try to achieve financial and economic stability by, in effect, pegging their monies to the dollar (or gold/silver in the past.) This tends to force politicians and central bankers to be disciplined, and also for the country to attract investor confidence. By definition, this kind of system is a more-or-less fixed exchange rate system.
The US, being effectively 'the issuer of gold' and holding the most power and wealth, is not as afraid of exchange rate instability. In times of instability, money tends to flee to the dollar, so there is a natural counter-balancing effect to keep the US system stable. In fact, the US can easily benefit from such instability, as holders of dollars often buy foreign assets on the cheap during crises.