Don't use the apostrophe. It's not "the report belonging to Reporters Without Borders", it's "the report written by Reporters Without Borders".
It's the same as, for example, "The Mitchell Report" (there are actually two investigatory reports by this name) - we wouldn't refer to it as "the Mitchell's Report".
Note that this rule does not always apply. We would say, for example, "Shakespeare's Romeo and Juliet" but we would not precede it with an article. We would, however, say "... the Shakespeare play, Romeo and Juliet". Here, "the Shakespeare play" functions the same way as "the Reporters without Borders Report".