There are many cases where the jews were sent back to Germany because foreign countries did not accept them. If you could answer why they sent them back (either France UK or the US) and if they could have done more I would be extremely grateful.
They sent them back because of normal immigration procedures. Most people who got in were relatively influential or powerful until later in the war.
The US accepted a good bit. But the pressures of the Great Depression limited the amount of refugees that governments could allow in.
History of French anti-Semitism ignited by the Dreyfus Affair which divided the country. France had accepted a lot of foreigners in the 1920s and early 1930s to replace the workforce lost during the war. Depression hit and anti-Semitism and xenophobia grew. Began to remove the French citizenships of foreigners as they became a scapegoat for the economic and employment problems which France had. French PM Daladier introduced some racial segregation laws in 1938. When under occupation, Vichy continued this trend and went above and beyond the Nazis' expectations. The French police even rounded up thousands of Jews themselves before keeping them in horrific conditions and sending them to Drancy and then Auschwitz in July 1942. So to sum up. France didn't accept Jews from Germany because they were just as unwelcome.