Immigrants commit less crime than natives do. Whether it's Denmark, United States, England or France. However the succeeding generations, their children and grandchildren, will normalise to the same level of crime natives commit relative to their socioeconomic background. The reasoning behind this is because immigrants tend to face harsher punishments for committing crimes (like deportation) so they're more careful than natives are. This pretty much kills the idea that criminality is inherent to culture or something more intrinsic (criminality linked to "race" or ethnicity).
Also, look at Switzerland whose 25% of the population consists of immigrants. However, they don't face the same issues with minority related crime France and England do. Why? You should look at the recent history of the immigration boom in the second half of the 20th century. Countries like France, Belgium, England, and so on were facing a labour shortage so they decided to make that up with opening up low skilled immigrations from countries all over the world. Normally they're not going to place these arrivals amongst the middle and upper class section of the native population, they're grouped up and placed amongst the poorest in poor communities - slashing their opportunities to social mobility because their neighborhoods are isolated from the same public services the rest of country has access to. This along with them being low skilled, acts as barriers to entry to the "majority culture" and labour/economic force of the host nation. This is why you consistently see people of [Polish, Czech, Romanian, Greek, Turkish, Moroccan, Nigerian, Algerian, and Carribean islander] descent with the same levels of income and same type of neighborhoods exhibiting the same statistics across a variety of areas (criminality, education, employment) ; despite all being entirely completely different ethnic groups.
The issue is socioeconomic and infrastructural, not cultural or biological.
