It is noteworthy to consider how the European Right focuses less on a specific Christian narrative and instead casts Christianity in terms of the overall Western 'intellectual' heritage. The Christianity they wish to preserve is the synthesis that occurred in the 18th and 19th century when orthodox forms of Latin Christianity (both Roman and Protestant) underwent a transformation and were blended with Enlightenment epistemology and ultimately classically Liberal values.
This period, coupled with imperialism and industrialisation set the stage for modern European society. It's this 'bundle of ideas' that is being preserved and at this point is to many, represented by something so mundane (and ironically sacrilegious) as a crucifix.
They want the immigrants to understand that they must integrate into the existing cultural milieu and they will not be catered to. This is still a form of pluralism but one in which the majority holds a definite sway. This is a populist dominated form of cultural authority as opposed to the principled and neutral/universal republican values the US Constitution is supposed to represent.
The French of course believe their republicanism represents universal values but they believe those are best represented by French culture. All the nuances are fascinating. Even in the American scene there is a difference between those in the Christian Right who retain a Christian-America first style of pluralism which would make immigrants welcome, able to function, but second-class and the growing forms of open theocratic rule which would call on the state to suppress dissidents and any form of ideology that does not comply with the Christian state. The latter is still a small minority but the radical climate is certain to give it a boost. The perceived Muslim ban is in line with their thinking and represents the kinds of measures they would like to see implemented by the government.