We studied Blum in my history class, and I'm just curious.
The most obvious reason is that the only real opportunity for a Franco-German conflict in 1936 was over the remilitarisation of the Rhineland in March of that year. This was in flagrant breach of the Versailles Treaty and the possibility of war was publicly broached in Paris. However, the Popular Front didn't ascend to power until June 1936, months after the crisis had passed. It was the Sarraut government that was responsible for the climb-down over the Rhineland.
That said, there are a couple of factors in the decision of Sarraut's government to avoid conflict that are worth noting, as they were influential in the Popular Front's later foreign policy:
In this context, French diplomats were quietly satisfied with the Rhineland outcome, given that it led London to begin talks on strengthening military commitments. They were quite happy to use British reluctance to engage itself in a European war as a means of escaping their own commitments in Europe. This continued throughout the Popular Front period, with London acting as a convenient sobering influence (ie with regards Spain, Austria and Czechoslovakia).
These concerns only sharpened after the victory of the Popular Front. Despite Blum's protestations that he was the "loyal manager of capitalism", the fact of the Popular Front's victory and the accompanying worker factory 'occupations' damaged business confidence. Something not helped by the government's actual policies in the space of the economy and social reform. Any industrial recovery came to a halt and, in addition to currency crises, the Popular Front had to contend with capital flight and employer hostility.
Neither of the above factors are exhaustive [edit: they, for example, skip over entirely the issue of the SFIO's pacifism] and nor are they intended to be a summary of why the Rhineland Crisis didn't spark a war. But taken together I feel that they formed key constraints on both the Sarraut and Blum governments. They were obviously mutually reinforcing: economic and social turmoil at home fostered a political reluctance to go to war (alone), which in turn increased a dependency on London. This dynamic very much encouraged caution in foreign affairs, even when there was strong pressure to act, as in Spain.
(All quotes are taken from Julian Jackson's The Popular Front in France.)