The Concordat of 1801 was an agreement between Napoleon and Pope Pius VII, signed on 15 July 1801. It remained in effect until 1905.
In Germany, people would refer to it as "Drittes Reich", which is translated in English to "Third Reich" - and I think this is the answer you are looking for, it's very widely used.
Reich means "Empire" , so it could also be translated to the "third empire" but this is not usual.
A. Ferdinand and Isabella