I agree with Richiev and dpg. Writing a story that is seemingly set in our world would have our history. Changing something (somewhat unnecessarily tbh) like this will make readers just focus on the inaccuracies rather than the story.
What difference does it actually make for him to be the 2nd? Or 3rd? or 4th? He's already breaking ground in being the first American Pope... the simple fact that he's abdicating for the woman he loves is the story. Not how many others have abdicated before him.
Don't let a potentially good story be sidetracked by a minor point that is really not worth fighting for.
The fact that he's an illegitimate son of a billionaire... is that important?
It is probably unlikely that anyone here is going to read your script (I've asked the very same question when I first joined). The whole point of a logline is that a reader can understand the story enough so they don't have to read the script. A logline is the first thing a person will read so it's really important that it's as good as it can be and that's the?primary purpose of this site. To help nail a good logline. However it's always worth remembering that a great story can have a bad logline ?but a bad story can never have a great logline.
From my own painful experience too, always write the logline first. If story issues are pointed out here based on your logline - no big deal - you're tweaking 35 words. If something is pointed out in a logline and the script is written.... could be a disaster.
Hope this helps.