Also, the left in Europe isn't necessarily pro-immigration. Immigration is a progressive leftist issue, while a lot of Europe's left is more concerned with economical leftist issues. See e.g. Denmark, where the Prime Minister is a social-democrat with pretty strong views against migration.
Actually, I just found a quote on Wikipedia from her (Mette Frederiksen) that beautifully captures my point here: "For me, it is becoming increasingly clear that the price of unregulated globalisation, mass immigration and the free movement of labour is paid for by the lower classes."
So in that sense, I agree with
@Rajma that the continuation and intensification of immigration issues might lead to a stronger stance against immigration from part of the European left (generally the centrist part that is closer to power), removing a key attraction of rightist populist parties.