Why did Great Britain and France sit on their hands after declaring war on Nazi Germany following Hitler's invasion of Poland?
The major reason why Great Britain and France did not do anything was that there was very little that they could do. When Germany attacked Poland, there was no plausible way for the Allies to actually do anything to help that country.
There were two reasons for this. One was military and the other was geographical. On the military side, the French and English were simply not ready to conduct any kind of operation to relieve the pressure on Poland. They had been hoping that they would not have to go to war and were not prepared to start serious fighting in September of 1939. They were certainly not ready to do anything like invading Germany to relieve Poland.
On the geographical side, it would have been impossible for them to directly aid Poland. There was no way that France could get overland to Poland to help fight there. The British or French could potentially have shipped troops to Danzig, but shipping enough troops and materiel to matter is a huge undertaking and there was no way that either country was ready to do that.
Basically, Poland was too far away and the Allies were too unprepared for war. Therefore, they “sat on their hands.”