Great question! The answer to that is the "Air Force One" callsign is reserved for planes carrying the US President WHEREVER they fly, whether it be to an ally state like France or a far-away distant regime like Myanmar.
It is true that other states also have their own "callsign" for planes carrying their heads of State/Government. But it will not use the "Air Force One" callsign. For example, Canada calls their jets carrying their Prime Minister "Can Force One", France calls it "Cotam One", and Japan calls it "Japanese Air Force One" (it's a long-ass name but they had to call the whole callsign!), etc. Conclusively, I am not sure if it is an international agreement or how the US managed to keep the callsign very exclusive to themselves and enforce it in foreign airspace, but you will never find a second "Air Force One" callsign.
Hope this helps!