Hi, unfortunately I cannot provide the best answer because as an East European this has never been an issue for me and furthermore, I have not arrived on campus yet.
Anyway, the second most common nationality in INSEAD is American (IIRC, too lazy to fact-check right now), so there are plenty of Americans there. Many professors are American; the school uses a lot of US case studies. That being said, many of the American students are second generation immigrants, or have dual nationalities, or have lived a significant amount of time somewhere abroad.
All of the INSEAD students I have spoken to have been exceptionally friendly and open-minded. I guess that when you attend a school with such a diverse student body, you learn not to assume anything about a person just based on his nationality and background. You have students from all over Europe, from the Middle East, from India, China, Russia, Americas, Australia - I am looking at the directory and there are admits in my class from every possible part of the globe. But we share one thing in common; all of us have put a lot of effort and we are paying through the nose for the privilege to be in this diverse crowd. Therefore my guess is that no one, and I mean no one, at INSEAD is a prejudiced bigot.
Of course there are going to be lots of people who disagree with US policy. Maybe you will be dragged into arguments about that - just speculating here. Where exactly 'disagreement' turns into 'anti-Americanism' is anybody's guess and it depends on you as well.
My advice - visit INSEAD's stand at you local MBA fair and talk to the marketing people. Several of the girls working in marketing and in the admissions office are American, they should be able and willing to tell you about their experience working in France/Singapore. Also, try to reach any current students or alumni with background simiar to yours.
Hope this helps, PM me if you need stats from MBA Connect.