I do not know how the Pope's activity is covered in Western media, but local media in my country (Romania) covers all the important meetings of the Pope. Many of these meetings are with important political figures, as briefly caught in the images from here.
The title of this article clearly suggests that "Pope Francis is a man of peace - and immense political power":
the papacy has always enjoyed diplomatic clout. In the early 1800s, the Pope pressured heads of state to suppress the slave trade. In the Eighties, Pope John Paul II united Christians in opposition to communism. And Benedict XVI made overtures to the Eastern Orthodox – something that his intellectualism and love of liturgy made him especially well placed to do.
However, present times are quite different, as irreligion seems greater than ever in most of the developed countries (also see atheism demographics in Europe). Also, this article suggests a clear decline of Catholicism in the United States.
Question: How does the Pope influence today's politics in countries where State and Church seem to be clearly separated?
My assumption is that there is a clear political influence, since many politicians are "queuing for an audience" with the Pope.