Question:
Answer:
We can know by examining whether a papal claimant was validly elected according to the election process confirmed by his predecessor(s). In the case of Pope Francis, he was validly elected in March 2013 by two-thirds of his fellow cardinal electors, as prescribed by his predecessor Pope Benedict XVI.
You refer to the Western Schism—also known as the Great Schism—when there were as many as three claimants to the papacy. This crisis began after the death of Pope Gregory XI in 1378 and was finally resolved with the lawful abdication of Pope Gregory XII and the subsequent election of Pope Martin V, both in 1417. All along, to anyone looking at the matter objectively, it was clear that there was only one validly elected Pope at any one time during this period.
For more on this subject, please see this article by Canon Francis Ripley and also this response by Father Charles Grondin.