Toward Ecosophy

The French Army of today is not the Army of 1958 that overthrew the Fourth Republic and brought De Gaulle to power. It is tiny by comparison, all professional and largely occupied outside the country, especially in the Maghreb. Nor is there any issue (like Algeria in 1958) which could provoke such a conflict. That said, the elite regiments of the French Army still recruit overwhelmingly from the traditionalist Catholic upper middle class and the aristocracy, and are part of families with a strong presence in the French establishment. They tend to overlap with the right-wing traditionalist Catholic readership of Valeurs Actuelles.
I think it's history rather than current events that make people worry about the role of the military. The "Chef", the military saviour, is a powerful archetype in French history. Pétain played this role in 1940 and De Gaulle in 1958, though for very different purposes. I can't see a military coup happening (and I can't see it succeeding anyway) but the possibility of some kind of backlash is very strong. Essentially, we have, and have had for some years, a PMC government with different front-men. The Right screams that candidates of the alleged Left are Communists, the Left accuses the Right of fascism, but it's largely for show. In reality, France has moved steadily in a neoliberal, largely Anglo-saxon direction since the 1990s, mixing economic insecurity and identity politics with massive transfers of resources to the rich. After a colourless bureaucrat (Hollande) and before him a petty crook (Sarkozy) we now have a technocrat managerialist President who really wants to be Zuckerberg, and surrounds himself with young, largely inexperienced, advisers who think they're in a start-up. There's a very real sense of fin-de-régime here, and people are already talking about a Sixth Republic.
But although that idea started on the Left, the parties of the Left, always hopelessly divided, are at odds with each other with only a year before the Presidential election. Whilst several groups (notably the Socialists and the Communists) are actually showing signs of a return to genuine class politics which would be popular with the voters, as well as being prepared at least to talk about problems such as immigration and terrorism, much of what trades as "The Left" is just the soggy IdPol arm of the PMC, which seems to be going out of its way to alienate voters. (This includes the Greens).
So the initiative lies with the Right, and a strong candidate would probably defeat Macron next year. But the only declared runner (Xavier Bertrand) isn't evoking much enthusiasm. So people are looking elsewhere. The Right in France is as divided as theLeft, but there are those who dream of some kind of grand coalition which would unite the existing parliamentary parties of the Right, the traditionalist catholics and the new populist Right forces typified by Le Pen. The fact that Le Pen has welcomed the letter signed by the military is a straw in the wind here. Whereas Le Pen is too populist a figure for many, there is the possibility of a more acceptable figure emerging. The journalist and best-selling author Eric Zemmour, whose remarks could be taken to support mass deportations of immigrants, scored 17% in an opinion poll in February, which is extraordinary for someone who's clearly said he doesn't want to run. But it's an indication of how fed up the French are with their PMC leadership.
If someone feels like doing a chart for the French elections next year, the results would probably be very interesting.