More specifically, when did Maurice Duverger first use the term ‘semi-presidential’?
I have been doing some digging in Parisian libraries and the answer, so far, seems to be 1951. He refers to Weimar Germany being a semi-presidential regime on p. 431 of the first edition of his book Les partis politiques (Political Parties).
It is also possible to get a sense of how his thinking evolved. For example, in 1949-1950 he gave a series of lectures on political parties at the Institut d’Etudes Politiques in Paris (Sciences Po). The text of the lectures is available and they clearly led to his book as they cover much of the same material. However, in the equivalent place to where the Weimar Germany reference is made in Les partis politiques, there is no reference in his lectures. So, presumably, he decided to call Weimar a semi-presidential republic (in print at least) around 1950-1951.
Also, in his 1948 Lectures on Constitutional Law in Bordeaux on p. 115 he does not call Weimar semi-presidential, but he does say that the parliamentary regime there came close to being a presidential regime. So, he clearly has Weimar in his mind as a mixed system as early as then.
Duverger maintains his reference to Weimar as semi-presidential throughout the various editions of his Les partis politiques book. I am now trying to find out when he extended the term to describe the system in other countries, including France, so as to see whether he did so before he introduced the concept of semi-presidentialism and systematically identified a set of semi-presidential countries for the first time in 1970.