Interesting that you point to the Boulanger and Panama crises as points of greater danger for the republic.
Not necessarily in the sense it would cause the republican regime to collapse, although we could argue the Boulanger crisis could have this effect if things went immensely bad, that they were confidence crisis in republican institutions (and notably the Chambre des Députés and the parlementarian regime) that were still fairly recent and debated in the 1880's, giving a lot of momentum to illiberal, authoritarian (moreso than anti-republican) or nationalist movements.
With the wrong events at the right time, there's nothing preventing the nascent IIIrd Republic to have turned sour, these likely in a republican form but one that would at least turns the clock back to 1875, that is by enforcing the constitutional powers of the president and of the Chambre (the engineered presidential incompetence and the dominance of the Chambre were not set in the constitution, but a matter of informal constitutional agreement) : and that's a minimum, as you could end up with a fully executive semi-democratic republic (in the sense of Imperial Germany), a fragilized and staunted civilian society (as with Italy), watered-down bonapartism, etc.
Had Boulanger come 'on horseback' to become dictator of France, for how long would this have likely eclipsed democracy and liberalism in France?
To be honest, I don't think that's a vraisemblable outcome : boulangisme was more of a standard for a very diverse and self-contradictory ensemble of revendications ranging from semi-bonapartism, nationalism, socialism, monarchism, etc. (basically anything but radical and liberal republicanism) that would prevent a massive popular and institutional support for a full blown military coup. Although a failed boulangist coup in 1889 could have interesting consequences.
An electoral victory for boulangisme, by staunting the radical/moderate counter-fire of 1889, however... That would be an interesting view insofar socialist movements weren't well defined or distinct from overall populist movements by then and would have an hard time challenging a boulangiste, semi-bonapartist, bloc in which monarchists, bonapartists and anti-radical/moderates could recognize themselves in while banking on successive confidence crises (corruption, antisemitism, etc.)
Notwithstanding the likeliness of a successful boulangiste coup, you could expect populist values to be much more important in contemporary French political life. Not necessarily to the point of caudillismo, but certainly challenging parlementarian and liberal values.