You might be interested in some previous threads on the topic of British and French actions after the Soviet invasion of Poland:

Britain, France, Poland, and the 1939 Soviet Invasion

• Why didn't Britain/France declare war on the USSR at the same time they declared war on Germany at the start of WWII? - 10 comments, over 11 months old.

• Besides the topmost comments linking to another thread, at the bottom there is a summary of the military situation, an analysis of the specific wording of the treaty between between Britain and Poland, Franco-Polish relations, and the timescale of Poland's defeat.

• When Hitler and Stalin divided up Poland, why didn't France and Great Britain declare war on Russia as well? - 29 comments, over 1 year old.

• A primary source is quoted at the topmost comment and commenters engage in debate over the legality of the situation.

• Why didn't the Allies declare war on the Soviet Union when the latter invaded Poland in 1939? - 10 comments, over 2 years old.

• The topmost comment is a one-liner that succinctly states the legality of France and the UK's lack of action.

• WWII started when the UK and France declared war on Germany for attacking Poland. But why didn't they also declare war on the Soviet Union? The USSR also attacked Poland. And the free and democratic Finland as well. - 45 comments, over 8 months old.

• This thread goes for a realpolitik and military interpretation of the situation to explain why France and Britain did not declare war on the Soviet Union.

• Why didn't Poland's allies (Great Britain and France) declare war on Germany, but not do anything for over a year? Also, why didn't they declare war on the USSR? - 8 comments, over 1 year old.

• Commenters here describe Stalin's motive for the 1939 invasion and how it appeared to the British and French governments.

• Why did France and Britain only declare war on Germany when the Soviets also invaded Poland in 1939? - 9 comments, over 2 years old.

• This thread puts the Soviet invasion of Poland into context with Britain's declaration of war against Germany after Germany launched its own invasion.

• Anglo-Polish Military Alliance Pact - did Britain and France fail to uphold their side of the pact? - 9 comments, over 2 years old.

• This post puts the treaty in context and also delves into a counterfactual scenario involving a quicker, more committed attack by France at the start of the conflict.

• The Allies declared war on Germany in response to their invasion of Poland, as per their defence pacts. Why did they not also declare war on the USSR who invaded Poland at almost the same time? - 4 comments, over 10 months old.

• There's a very brief summary here that also mentions a plan to attack Russian oil facilities that was aborted after the Battle of Poland.

• Why didn't the Western Powers declare war on the USSR the same way they did on Germany, when the two invaded Poland in the beginning of WWII? - 33 comments, over 2 years old.

• This thread delves into a military counterfactual debate about what the Western Allies could have done during the invasion of Poland.

• France/England/Poland Defensive-pact 1939 however no declaration of war against USSR? - 5 comments, over 1 year old.

• This thread highlights several operations planned by the Western Allies to attack the Soviet Union after the invasion of Poland.

Reprecussions of the Invasion

• Why is that only Nazi Germany is condemned for invading Poland while the Soviet Union also annexed a large portion of Poland and committed nearly half a million troops? - 4 comments, over 5 months old.

• A commenter in this thread goes into the long-term ramifications that the Molotov-Ribbenrop pact and 1939 invasion of Poland had on the USSR's image during and after the war.

• Which occupation zone was worse to be in? Soviet occupied or Nazi occupied Poland? - 11 comments, over 6 months old.

• Commenters here compare and contrast statistics, policies, and intentions between the two powers.