I think Americans interested in studying overseas to begin with (and I'm not one of them) probably don't feel the same way as the freedom fries lovers in Congress and elsewhere.
I am an American interested in applying to INSEAD down the road and this has much to do with my background of being born and raised overseas, and my desire to work abroad in the future. Whether the admissions committee at INSEAD will penalize me for my current occupation as a US military officer given the political tensions of the recent past remains to be seen. It is my hope of course that my application be viewed for its merits and politics would not be a consideration.
All things aside, I kinda believe (and I don't know this for a fact, so there's a chance I could be wrong), but I think there are millions of people in both the United States and France that can't really control what our politicians do other than at elections as long as those politicians are still following their nation's laws. I think academic institutions would take the same reflection on international applicants. I just think Americans are scared to go abroad because they don't want to get blown up. As for whether anyone cares, I personally don't care if there are international students at my school either. I just want smart, fun students.