A leading Spanish Muslim Abdelkarim Carrasco says "[e]ither Europe develops and supports the idea of a mixed culture, or Europe has no future... Europe has to learn from what the United States has done. It is a country that has taken in people from all over the world." (For some reason, the NY Times left off the second part of that quote.)
This is the crux of the whole issue, isn't it? If I was at home in New York I think I'd probably see this as a potential solution, but from here it's clear that this is not as easily done as said.
Americans do assimilate immigrants more smoothly than does any European country. There are many reasons why this is so, some of which are government policies. But, one feature of America's success that I don't think is possible in Europe is the relative ease most Americans feel about their country being transformed by immigration.
Sure it's not trouble free, but Americans are less concerned about the effect immigrants have on society than are Europeans. This is because Americans have a less fixed idea as to what their culture is than do Europeans and, therefore, they are less worried about the changes immigrants bring.
The white, Protestant society of 1840s America is gone. Also almost totally gone are those who think that's how America should be. America was much more Anglo and/or Germanic in the 1800s than it is today. European nations have only recently begun to experience anything like that. And, their cultures are much older than America's culture.
There has been so much glib talk about assimilation. Muslims are failing to assimilate or the French government hasn't been doing enough to assimilate Muslims. It's just not that easy. Assimilation means (a) there has to be some cultural identity that the immigrants can aspire to and be welcome in and (b) that the majority culture is happy to be changed gradually.
You can see this in America with simple things like general acceptance of Spanish phrases and Mexican foods and brand names. These things would have been unthinkable in the 1950s.
Can this happen in a country that has a government run academy dedicated to the preserving the purity of the French language? Right now they're not happy about anglicisation, but what about arabisation? I can just imagine how they will react if Arab words and phrases begin to gain common currency.