There were waves of migration within Europe before WWII, that sometimes created some tension but by and large it only took a generation to assimilate them because in general (1) they made efforts to assimilate and (2) cultures were close enough that it wasn't too difficult.

An example is Italian migrants to France (and other European countries) in the late 19th and early 20th century.

What has happened since and is still happening, is a combination of continuously very large numbers of migrants and lack of assimilation.