I don't have my history books open, but I think USSR invaded Poland several weeks after Germany did, and a couple of weeks after Britain and France declared war on Germany. Also, this meant the Allied nations were then preparing for a war on the Western front. This is evidenced by the fact neither Britain or France sent any support to Poland (despite having a pact to do so, at least in Britain's case).
Was Poland just an excuse for Britain and France to declare war on Germany? Maybe, but either way it is likely those two nations understood creating another front on the East would not be tactically possible. Scared of USSR? Unlikely, but maybe scared of fighting Germany and USSR at the same time. It is known Britain did not want a war with the USSR, most likely because it would have been a terrible war. When the UK agreed to aid Poland if a European nation invaded, it was specifically stated this only referred to Germany, and not the USSR.
I think there is also something floating around that Britain expected the USSR and Germany partnership to go belly up and USSR would be a major help in the war effort against the Nazis. I think fear is the wrong word to describe Britain and France's actions. It is worth remembering at the time, Britain was the major superpower, albeit on the wane. Hitler is officially known to be actively cautious of the UK and tried at all costs to avoid conflict with Britain. Again, scared is probably the wrong word for being astute.
