I have managed to gain a copy of the text where Google Scholar records the first ever reference to the term ‘semi-presidential’.

The article is called ‘A Scrap of Crimean History’. It is written by D. Christie Murray. It appears in The Gentleman’s Magazine, New Series, vol. 14, Jan-June 1875, pp. 171-183.

The author, whom I assume to be David Christie Murray, appears to have written a number of novels around that time. He would also appear to be the author of ‘With Fire and Sword; A Tale of the Russo-Turkish War; By One Who Went Through It’ that was published in 1880 in the children’s magazine Union Jack. The subject of this later work seems to draw upon the same material as the article in The Gentleman’s Magazine. While The Gentleman’s Magazine first appeared in 1731 as a serious publication, my sense is that The Gentleman’s Magazine, also known perhaps as The Young Gentleman’s Magazine, was refounded in the mid-late 19th century and was also aimed at a younger audience.

The Crimean War saw the first systematic examples of what would now be called ‘embedded journalism’. While the article in the Union Jack suggests that Mr Murray was present in the Crimea, it is puzzling that his story is only published some 20 years after the war. This seems to suggest that there is a sense of ‘fact and fiction’ to the article, rather than war reporting per se.

Anyway, in the article, Mr Murray is describing the situation in the Crimean War (1853-56). On p. 178, he writes:

This is hardly an auspicious academic start for the concept of semi-presidentialism, but it is interesting that right from the outset it was associated with France and a particular, though hardly rigorously specified, type of leadership.