The two popes in the Leviathan series play a minor roles in the books and are only mentioned by various characters in the series.
In Leviathan, the pope had written a scroll before the book begins declaring that Archduke Franz Ferdinand and Princess Sophie's children be given the ability to become the successor of the current Emperor of Austria-Hungary on the terms that the scroll would not be revealed until after the emperor's death. This scroll was written during Franz Ferdinand's visit to Rome with Count Volger. Whe Prince Aleksandar arrives in Switzerland with his men in their Cyklop Stormwalker after his parents' death, he learns from Count Volger of the scroll which would be able to elevate his status from Prince to Archduke.
In real life, the pope was Pope Pius X.
In Behemoth, at the end of the book, Alek learns from Count Volger that the pope has died, thus resulting in a possibility that the scroll might be meaningless. They hope that his succesor will not have an ear with the Germans, which would make him more likely to ignore the scroll. In real life, Pope Pius X's succesor was Pope Benedict XV, who was largely anti-war and declared the neutrality of the Holy See during World War I.