In the annals of insignificant matters, this item figures right up there near the top: It bugs me that so many journalists and other writers, even those writing for bigtime media outlets like this one, are calling the new pope "Francis I." He's not Pope Francis I. He's Pope Francis. Even the Vatican says so.
Why not "The First"? Because there has yet to be a second. You can't be the first of something until there has been another of the same later. In the United Kingdom, for example, Queen Victoria will never be QVI until there is a Queen Victoria II. The same rule concerning monarchical names holds true in Luxembourg and Norway.
People make this same sort of mistake when they plan an event. They'll say, "Let's call this 'The First Annual Neighborhood Spaghetti Dinner." But it's wrong to call it that until there has, in fact, been a second one. What if the organizers the next year decide to serve eggplant instead? Or they all get hit by a meteorite and no dinner gets organized? If, in fact, there is another spaghetti dinner the following year, it would be correct to call it the Second Annual Neighborhood Spaghetti Dinner. And, with the second having occurred, it would then be okay to refer to the first one with that ordinal honorific.
Purists might argue that this rule regarding ordinals is not universal when it comes to monarchies, or even papacies. And that seems to be true, as the Wikipedia article on Monarchical Ordinals points out (yes, I know: I need to get a life). Contrary to the practice in places like the United Kingdom, "Other monarchies assign ordinals to monarchs even if they are the only ones of their name. This is a more recent invention and appears to have been done for the first time when King Francis I of France issued testoons (silver coins) bearing the legend FRANCISCVS I DE. GR. FRANCORV. REX." It's the practice in Belgium and Spain, and has been used in Brazil, Italy, Mexico, and Montenegro - and also, I guess we should note, by the Papacy under Pope John Paul I.
But all this is quibbling. As noted above, the Vatican made it clear that the new pope is Francis. Not Francis I. So, that's what he should be called.