Small fix: Republicans weren't only Communists. There was several republican factions. Most of them were leftists, but not Commies
Firstly, equal small fix in that the nationalists were by no means all fascists either. Both sides were a complicated mixture of political/social/regional/religious/ethnic and other ideologies and identities.
Really, though, I think the OP's question needs tweaking - you don't need a longer SCW to get foreign involvement (which is what they are aiming for here). OTL the war went on for two and a half years without spiraling out into a global conflict. Whilst a Spanish Civil War still going on in September 1939 might see foreign involvement it might equally not ("let them get on with it") and might even delay or alter the starting of WWII in Europe. Plus the Molotov-Ribbentrop pact will make this complicated in 1939.
The main question, then, is how to get the powers of Europe involved beyond fighting a proxy war as OTL.
Britain would be the hardest - not only was the Government committed to non-intervention, there was very little popular appetite for war in 1936-1938 more generally. The Labour opposition is still largely pacifist in nature at this time. Moreover, whilst the mood in the general public might have been slightly inclined towards the Republicans, the Governments and powers-that-be were more supportive of the Nationalists, leading to a bit of an impasse.
France might be easier to involve - they were already quite upset about Italian and German involvement in the conflict. The problem was that the French looked to Britain for guidance.
Germany, Italy, and the Soviet Union - were all content with fighting this as a proxy war, so you would need to have a POD that would encourage them to take action.
Potential PODs:
There are quite a few though:
* Have Franco-Soviet relations markedly improve in the 1920s and 1930s, maybe at the expense of Germany. Have collaboration between the Nazis and the Soviets over trade in the 1930s fall through meaning that the Soviets see Hitler as more of a threat and France as more of an ally. This means that France could feel more confident about intervening.
* Have the French Popular Front be more stable and decisive. OTL they were worried about the potential of revolt on the extreme right in their own country, meaning that Blum could not through open the border with Republican Spain to arms trade as he wanted.
*Have Mussolini move against Albania or Yugoslavia earlier. Maybe 1936-7 after feeling confident post-Abyssinia. Internationally UK and France won't intervene beyond trying to force a compromise, but they will see Italy as much more of a threat to be countered. It might also see Mussolini be even more committed to piling troops and weapons into the SCW than he already was OTL.
*My personal favourite (I've thought about this for a timeline) - have Labour elected in 1935. Hard to do, although they did surge in the polls, but with a Labour Government softly supportive of the Republicans in place in 1936 the tensions are going to be much more present. OTL elements of the Royal Navy played a bloody dangerous political game in offering support to the Nationalists - sending them information, lying to British merchant ships trying to reach republican ports, allowing Franco to use Gibraltar as a signal base, and even using HMS Queen Elizabeth to physically block the Republicans from shelling a port that had fallen into Nationalist hands. OTL the Conservative Government was happy to let the matter lie, but with more support on the left for the Republicans (combined with a general suspicion of the armed forces in general) a Labour Government would probably have to act.