Just about every one of the occupied countries did that, even Denmark. There were always non-Jews to accommodate the Nazis quotas. But unfortunately, some Jews were willing to do that as well. Jacob Gens was Chief of the Jewish Ghetto Police in the Vilnius Ghetto is what is now Lithuania. He believed that accommodating the Nazis would save Jewish lives, so he encouraged the people in the ghetto to show up so they could be sent to "work camps" in Estonia. Gens told the people: "A Jew with a job, is a Jew with a future."
Despite being warned by resistance fighters in the ghetto, that he was sending people to their deaths, he didn't believe it, and continued his work to supply the Nazis with the quotas they demanded. One day when he was 200 Jews short of the required number, he called the 200 newly sworn in auxiliary police to the ghetto gates. He told them that they would meet the person who would lead them to the Jews that were hiding. Of course once they got to the gate, they were surrounded by Nazi soldiers, and realized that they were the missing 200 Jews, and were shipped out. When it was reported in September 1943 that the ghetto would be eradicated, the Nazis arrested Gens, and shot him the next day. That's what happened in just one ghetto.
About 75,000 Jews were deported to Nazi concentration camps and death camps and 73,500 of them were murdered, but 75% of the approximately 330,000 Jews in metropolitan France in 1939 escaped deportation and survived the Holocaust, which is one of the highest survival rates in Europe.
Which begs the question, did so many Jews survive in France precisely because the French were in charge of the roundups, as opposed to the Germans?
“Just about every one of the occupied countries did that, even Denmark.”
No, the Danes smuggled their Jews to Sweden.