The diversity train is a relatively new phenomenon.
EU expansion to the East had many factors. One of them being to have less barriers to get a cheap seasonal workforce pick vegetables in western EU countries [1].
Go back a few more decades: Germany in particular asked hundreds of thousands of people from Turkey to immigrate into Germany to help rebuild it after WW2. It's now the biggest foreign-origin population in Germany.
Not sure about France though.
[1]: https://www.nytimes.com/2017/12/11/business/europe-labor-rig...
Not quite, because the earliest wave of Turkish immigrants came after the migration agreement between Turkey and Germany in 1961 (and Germany was rebuilt at that time). The reasons for this agreement – initiated by Turkey – were curiously complex and not simply economical ones.
As a person whose parents are from India I take offense to the idea that family values in western countries are somehow incompatible with immigrants, both of my parents came to the US separately and decided to get married and have kids out of their own volition. Europe obviously has separate problems and migrant workers aren’t exactly the same as tech workers from India coming to the US but just because other cultures are different doesn’t mean they’re from alien planets or something.
Although I am sympathetic to Indians, I think people in India would not like it if a lot of Europeans showed up. It says here that Indians are 3.1% of the population of Great Britain https://en.wikipedia.org/wiki/British_Indians. I can't imagine Indians would appreciate it if 3.1% of India were European immigrants. Neither would people in a lot of other countries. I think people in the West have a right to their own culture if other people do because the nation of immigrants propaganda is revisionist. Japan has chosen not to import people. I don't think the choices are to let people in or die.
I think the actual reason is something like a vast western empire promoting diversity as a good thing for your country. The 2015 immigrant surge into Europe was not because EU countries needed workers. Similarly, countries that have tried to block immigration like Poland and Hungary are accused of being far right fascists and uncooperative and NGOs from the US come after you. The general belief seems to be that too many white people is a bad thing and backwards.