One of the reasons I wrote this was because there was a lot in Russian press about these "nationalist" parties being successful in the EU parliament, so I wanted to explain...
I feel that Russian press simplified this a bit. Also it might interest Americans.. None of this has anything to do with Nazism!

So, two more things are worth noting about these types of parties:

EU parliament elections are DIFFERENT from national elections. People tend to vote for "wacky" special interests issues in EU elections, or they just ignore it.
People just generally use these elections to express their feelings about some particular issue.

A lot of people vote completely differently in these elections than they do in national elections. In national elections, their personal economy and situation guides their vote + practical considerations. EU parliament elections is more ideological, or related to people's special interests, or whatever questions the EU are dealing with at the time of elections.

So the following have much better representation in EU parliament than at national level:
Environmentalists/Green, Pirate Party, Communists, Anti-immigration, Anti-EU.
Otherwise you'd have to vote twice for the same party, at different times, in order to be consistent.

Plus, the Parliament does not have most of the power in Brussels. Most of the power is with the Commission which is NOT democratically elected at all - it's a meritocracy / nepotistic organisation. Those who got in either have friends in high places, or they passed the entrance exam and could "sell themselves. All the Parliament can do is to (sometimes) stop the Commissions ideas and sometimes (rarely) start their own initiatives.

The EU has a SERIOUS democracy shortage - it was originally designed as a trade organisation, not as a super state, and the level of democracy reflects that... It is one of the issues that people are angry about, to the extent that they understand it. Most EU citizens haven't the foggiest idea how the EU is actually governed.... The reason I know it is because I was once involved in a campaign relating to the EU.

Secondly, these Nationalist parties are more or less discreetly AGAINST some of the politically correct concepts that are forced down everybody's throat whether they want it or not.

I.e. "homosexuality is great", "multiculturalism is enrichening", "you can never be too radical as a feminist", "there is no moral dilemma in relation to abortions" etc.

Their values for these types of issues are more similar to Russia, or to European values from the 1970s. A lot of people agree with this, but there is no outlet for such opinions - so people express their dislike with the Politically correct agenda/censorship through their vote.

Hope this shines some light on the results from the EU parliamentary elections.
Since the EU isn't very democratic, it doesn't make a huge difference who actually even sits in the parliament, so there really isn't anything to worry about. The EU will continue EXACTLY as before, nothing will change.