Though anecdotal, that's pretty interesting given this Pew Poll;

http://www.pewglobal.org/2015/06/23/1-americas-global-image/

Which DOES show a stark increase in favorability after the Bush administration in many European countries. This increase in favorability that we saw/see in Europe doesn't neccisarily extend globally, though.

Given that European countries are generally far more liberal leaning, when a liberal president is elected in the U.S it shouldn't be a surprise that many favor the candidate who more aligns with their views. And if we're looking at that poll, it is interesting to note that the increase in US favorability among European countries happened as Obama was taking office between 2008 and 2009 -- there wasn't neccisarily an increase over the course of his administration. That kind of conflicts with OP's original statement that "America rebuilt its global image during Obama's years"....apparently it only took Obama being elected for many people to change their view of America to "favorable". I don't know what that is supposed to tell us...lol.