I've read that France was, at the very least, forming contingency plans circa 1936 or so for a fight with the USSR. They seemed to be under the impression that eventually they'd have to deal with Stalin if his sphere expanded. That's part of why I think the USSR and Europe would have eventually fought, nobody trusted Stalin.
The West was in fear of a USSR invasion for the entirety of the USSR's existence. AFAIK, when the USSR fell, they could not find any serious plans on a war of aggression in Europe in the Kremlin archive. Everything was on how they would defend themselves if they were attacked.
They were all in on KGB subterfuge and supporting communist orgs throughout the world, though.
As for what country was the most powerful in 1938, it's probably way too complicated to get an overall "winner." Without spending time checking numbers (outside of carrier counts):
The Brits had the strongest Navy, if you base it on WW1 doctrine, but the US and Japan had
new Aircraft carriers, making the British Navy obsolete, virtually overnight (
the UK built 1 modern carrier by Dec 1938). The Brits also needed it's colonial troops where they were, in order to keep those colonies subservient.
The French had the largest Army and the fourth best Navy in 1938, but their whole defense doctrine relied on the Dutch, who screwed them over by trying to stay neutral. If the Dutch had actually deployed it's military correctly, the Maginot line would have probably worked, and we would not be sitting here thinking they were worthless and weak.
Almost as soon as Hitler took over, he started building up his military. They were probably number 1 or 2 in terms of Army, some of which had been battle hardened in Spain and the modernity of their armor/gear was a major contributor. They were far behind on the Navy side of things, though.
The Soviet Army looked like it was purposely kept weak, as to not become a threat to the Kremlin (Stalin). It didn't help that Stalin executed various high ranking men in all branches of the Soviet military. I don't know exactly how far along they were in the mobilization process in 1938, but they may have been stronger than at least Italy! The Soviet Navy was not a priority for them and almost a non-factor.
The US had the strongest Navy with 5 modern fleet carriers in 1938, but a very small weak army still using ww1 gear.
Japan would get my vote (guess) for strongest overall in 1938. They had the second best Navy with 3 fleet carriers and a fully battle hardened army that had been fighting in China for years. Their Aircraft was some of the best at the time, with a lot of them in production. They skimped on armor, small arms, and other areas to use those resources on the Navy and Aircraft, though.