Not as much as you might think, argues The Economist in a long, Christmas-special piece about French anti-Americanism (article freely available to non-subscribers) :
In one 2004 poll, 72% of the French had a favourable view of Americans, more even than in Britain (62%) or Spain (47%). Some 68% of those questioned in another poll the same year said that what unites France and America was more important than what separates them. During the 60th anniversary of the Normandy landings in 2004, politicians were frosty, but the people at large showed an outpouring of gratitude to American veterans.
It’s true that there is a big gap between the view of the U.S. (pretty bad) and the view of the American people (quite good) in France, a sure sign that a substantial part of what is regarded as anti-Americanism is mainly driven by anti-Bushism.