Non-Americans know a lot of facts about the US. However, the evidence that non-Americans know a lot about life in the US is much thinner; you get exactly, and I do mean exactly, the same sort of stereotyped impressions of a complex country that Americans have of others. It's exactly the same because it sources from the exact same human brain patterns. We're all just human in the end.

I'd also observe that since the US has had such a large footprint, the interesting question isn't whether the French know our President, vs. whether an American can name the French Prime Minister. That doesn't scale properly, as it implies a standard by which the non-American wins by knowing one name, but the American has to know everyone. The more interesting question is does the average Japanese person know the name of France's Prime Minister, or vice versa? And that's staying comfortably within the world's top ten economies, hardly an unfair question. I suspect by this standard the US would look a lot less bad, though I would still be completely unsurprised to see it at the bottom of such a measure. It just wouldn't be such an extreme difference.