As far as I remember, he was very popular with the common soldiers as he had paid a lot of attention to their living conditions and pushed reforms to make it better to be a soldier.
Popular among conscripts for the reason you says, but not only there is a large gap between being popular and blindly loyal to someone : republicanism in France was a really popular feature and anything threatening it wouldn't be naturally accepted.
A bit like, if Trump would have lost elections and attempted a coup, even his most loyal followers would have an hard time swallowing the pill. Again, I don't exclude possible mutinies among conscripts that I mentioned above, but I very doubt it would launch a massive armed support.
Boulangisme was, again, extremely heterogen : bonapartist, radicals, non-marxist socialits, some legitimists (you'd notice that they were not representing most of the electorate, which was fairly under moderate republicanism). Anti-establishment is, by nature, so. A coup on these conditions would have certainly political repercussions, but would be a re-edition of 1851 coup without the possibilities to blossom.
Why? Mostly because the conjunction of social crisis (1848), political crisis (1850) wasn't there; the general distrust of bonapartism or whatever was called so would probably impair a military based coup (at the difference of 1851 where political institutions supported Louis-Napoléon; they certainly didn't then).
So, yes, he was popular but it shouldn't be seen as handwavium.
His revanchism was also a good point for many people, compared to other politician they felt were weak (AFAIR)
AH.com have an history of considering every Frenchman in the late XIXth as bound to kill any German in order to gain back Alsace-Lorraine, Rhineland, and their little dog too.
Long story short, it's a very flawed narrative, based on a nationalist one : it should be taken with a grain of salt.
Not that it couldn't have its importance, but to make it the main political stance in
Belle-Epoque France is flat wrong. Politically, anti-elitism played a more important role into the rise of
boulangisme.
In fact, most of actively revanchist officers and elites, people that really wanted to antagonize Germany as much as humanly possible, were quite distrutful of Boulanger, because it was seen as an anti-traditionalist populist.
As I remember it, he chose not to launch the coup. The Parliament was at his mercy, the crowd was there, but he made a conscious decision not to do it
I'm sorry, but you're really underestimating the strength of republican institutions in the late XIXth : a political crisis doesn't mean it was a vital one. Parliment was so threatened that when Boulanger was ordered to be jailed, he had to flee in Belgium and 22 September elections show that boulangism collapsed (72 seats) before republicans (366).