Evidence on economic impact of 2015 European refugee/migrant influx
I didn't see the evidences on the recent European immigration, but the event is similar to the Mariel Boatlift story in Card (1990):


  The Mariel immigrants increased the population and labor force of the Miami metropolitan area by 7 percent. Most of the immigrants were relatively unskilled: as a result, the proportional increase in labor supply to less-skilled occupations and industries was much greater. Nevertheless, an analysis of wages of non-Cuban workers over the 1979-85 period reveals virtually no effect of the Mariel influx. Likewise, there is no indication that the Boatlift lead to an increase in the unemployment rates of less-skilled blacks or other non-Cuban workers. Even among the Cuban population wages and unemployment rates of earlier immigrants were not substantially effected by the arrival of the Mariels.


That's for a 7% shock. In contrast, Europe experience a 0.1% shock in labor supply. Maybe the only difference we'd find will be in the areas where immigrants settle densely.

For more reading:


Card, “Immigration and Inequality”;
Card, “Is the New Immigration Really so Bad?”


In general, economists suggest that low-skilled natives suffer a bit from an influx of low-skilled immigrants (but again, we're talking about large numbers, >1% of population):




http://www.igmchicago.org/igm-economic-experts-panel/poll-results?SurveyID=SV_5vuNnqkBeAMAfHv