During the build up to WWII (which of course includes the period within which the Spanish Civil War happened) Vargas oscilated, probably on purpose, between a closer alliance with the US and UK, and increased relations with the Axis. This was reflected in his cabinet, with, for instance, Oswaldo Aranha being a fierce Americanophile, and Felinto Muller a staunch Germanophile.
But about 1937, he was moving to the right, both internally (having staged a self-coup and rescinded political rights) and in foreign affairs (with many signs of rapprochement toward Italy and Germany). At that time, with the US and the UK being neutral, and France only timidly pro-Republican, there would be little reason for him to be shy about pro-Franco sympathies. This was certainly reflected in his propaganda, that systematically demonised the Republicans and blamed the war on the left and on democracy.
On the other hand, the complete unpreparedness of the Brazilian armed services, the long distance from Spain, the small importance of Spanish imports and exports, the absence of any real objectives to be attained by the Brazilian State in the conflict, probabably combined with a comprehension that the SCW was merely a rehearsal for a more important pan-European conflagration, would counsel him towards neutrality, to keep a good negotiating posisition for the years to come. So Vargas' position reflected these contradictory tensions. Militarily, he didn't contribute to Franco's war effort; diplomatically, he maintained an official pretence of absolute neutrality but dialogated with the Nationalists, not with the Republicans; commercially, he was happy to deal with an illegal uprising; internally, he used the conflict for his own ideological needs (and sternly repressed any pro-Republican positions within the Spanish immigration to Brazil).