reject[ing] giving more power to the EU is not the same as being anti-EU. I think there's a broad understanding that the EU isn't perfect, but that it's better than not having an EU. Britain is the one exception to this of course, but that depends on who you ask ... but even of the 50% who voted to leave, a large %age of those didn't really take stock of what it entailed.
In The Netherlands Geert Wilders' PVV became the second party by size, but the rest of the mainstream parties refuse to form a coalition with them so they are pretty much always in the opposition. I don't like that type of party (we had the LPF, then PVV and in the future maybe FvD) but I have to admit that as long as they don't actually govern they have a very useful function in that they often point out painful truths or situations that the other parties won't touch for fear of seeming politically incorrect.
That's four countries out of 28, and the Polish government is losing popularity (my girlfriend is Polish, I visit Poland often) due to its ultra-conservative Catholic views.
Poland was one of the most pro-EU countries in the union, and it will be again. It has seen the benefits firsthand, regardless of a vocal minority of xenophobes.
Le Pen had big gains yes, and still lost because the country decided to vote tactically, together to stop a fascist getting any power. She lost.
Hungary I'll give you, because it has been hardcore right-wing for a long while and massively corrupt.