I all fairness, the short sentence “Person X with a fan in France” could just as easily be meant either way.

Probabilistically I wouldn’t be surprise that the fan that blows is more likely that the fan who is a person simply because everybody but a handful of people in the World do not really have legions of human fans they take pictures with, but once in a while some of them might in fact be mentioned along with the mention of a fan of the blowing kind.

It’s only the picture and us recognizing Lana Del Rey as a celebrity that lets us know it’s one kind of fan rather than the other kind.