Having spend much of the past 25 years living on the continent, various places:
Hardly any xenophobia of the English variety. EU immigrants from other EU countries don't stir up any resentment, more regarded as cousins.
However, there is increasing and broad concern about MENA immigration, with different social values. This is fuelling the far right.
The 1 million invited in by Merkel followed shortly by Cologne and many small-scale incidents has seriously damaged her reputation.
The EU welfare & health systems are contributory, not based on residence like the UK, so there is not the resentment of immigrants from other EU countries affecting public services, because they clearly help fund it.
The major EU governments seem to have belatedly realised the scale of the concern and the referendum was a massive wakeup about the dangers of the far right winning the arguments.
So, we may see the UK referendum causing the EU to reform, be more responsive to ordinary European citizens and more successful as an entity.
It also helps that they are rid of their most bolshy member, who has been disruptive and blocking progress throughout the last 40 years.
Bad news for the UK:
The French presidential election is in 10 months and all that looks likely to prevent Marine LePen being in the runoff of the final 2 candidates is “look how the British have suffered since Brexit !"
Especially because LePen’s presidential campaign includes the demand for a Frexit referendum.
Hence, the current French gov desperately wants to prevent rule-bending that would grant the UK a special Brexit deal.
Merkel will be far more sympathetic to them than the UK, especially with so many Brexit politicians claiming / hoping the EU will collapse - that's just a pipedream, but an irritating one to them.