A potential coup of his has a good chance of succeeding, yes. As for what happens next, well, that is very much in the air.
Boulanger had support across political divisions in France, beloved by both the far-left and the far-right. As I see it, he could very well establish a monarchy, but I'm unsure of the popular support of monarchism in the revanchist era. He had a good chance of that, yes, but if he decided that monarchism was too unpopular, and I think he would have thought so, he would simply establish a French Fourth Republic, with himself as the absolute ruler of France. Either way, he'd have a very unstable coalition between the far-left and far-right. I'm not at all sure how he'd try to appease both sides - perhaps one option is to pursue some kind of proto-fascism. Hopefully he'd die quickly, giving France a strong executive but not much else. No matter what, he'd pursue some sort of militarism in an attempt to defeat Germany and avenge 1870. Such militarism would result in nations like Britain looking at France with unease. War with Germany may very well occur within his lifetime, and I think he'd lose such a war.