Quite a lot of Americans see his presidency as a huge success. In Poland - on the contrary. He's regarded here as a weak president, who betrayed his Polish allies and helped to establish the dominant position of USSR in Eastern Europe. I am aware, that this view may be influenced by the widespread sense of national pride/Poland the Christ of Nations. Your opinions?
FDR's terms in the 30s were focused almost wholly on domestic policies as the Great Depression was the greatest threat to the US since the Civil War. Faced with such an enormous threat and as a carry over of the generally less internationalist 1920s, the 1930s are probably the era when the US was most isolationist. The US didn't give much attention to goings on in Europe or the Pacific, traditional areas of US foreign policy concern, though FDR did initiate the Good Neighbor Policy in Latin America in the 30s to try to undo the interventionist image of the US in the region.
This clearly changed as WWII got started. The US, unlike France and Britain, didn't have any treaty commitments with Eastern European states (notably Poland and Czechoslovakia). Thus, when the war started in 1939, the US didn't get directly involved. However, the fall of France shook the US as no one thought France would fall as quickly as it did. Thus, the US started getting more involved, mainly through supplying Britain, though it had not gotten directly involved yet. The US was limited in its involvement through the "boats for bases", Arsenal of Democracy, and lend lease supplying agreements.
The US and UK drew close between 1939 and 41 with FDR wanting to get more involved, but being bound in the US with anti-war proponents. The attack on Pearl Harbor in 1941 was a death knell to the anti-war groups, leading to the US involvement, first in the Pacific against Japan, and later directly against Axis forces in Africa and later Europe.
With all that being said, FDR was never very close with Poland. The US was closest with the UK followed by the USSR. The US had rocky relationships with the Free French Forces and Nationalist Chinese both due to who their leaders were. The US-Polish relationship was much more limited.
By Yalta, the USSR was already occupying and in control of Poland. The US was in no position to really do much about it. The British and French, after the war, made some calls for action regarding Poland, but the Soviets had established firm control over it. The 1948 Czechoslovak Coup could put more blame on the US, though the Cold War had not started in earnest yet.
In general, I think the Polish view of FDR that you presented is unfair. The US and Poland (and Eastern European states in general) were never particularly close. The US was never in a position during WWII or immediately after to help create democratic states in Eastern Europe. I think extending Western Betrayal to the US is unfair (and unfair in general).