If they don't like the culture in the country they move to, then why did they move there? I can't possibly imagine choosing to live in Saudi Arabia, so why do they want to move to the US or France?
Simple. They are commanded by the Koran to make the entire world the House of Ummah, which is to say, where Allah reigns completely. They must convert everybody in the world, with the exception of those they allow to live in Dhimmitude (second class slavery) or those who resist, who they must kill.
For Muslims, there is no peace except under the total reign of Allah and his Prophet. They cannot be appeased. All the hopes and wishes of non-Muslims to the contrary won't change those facts or commands of their scriptures. It is an essential part of their belief system they convert, conquer, and subjugate (or kill) the Infidel.
In other words, it's "them" or "us"!