My feeling was that the financial integration (ie. Euro) was unpopular in the southern countries. But none of the GIIPS countries even wanted out of the EU - just out of the Eurozone. Not even Greece during it's hardest years. I'll take that as meaning the fundamental nature of the EU is safe and stable, but obviously this is a matter of perception, so we can agree to disagree.
And even then
public support for the euro was generally pretty positive during the height of the crisis. It was mainly that
some politicians wanted out of the eurozone (I think during the height of the crisis polls consistently showed something like 70% of Greeks supporting the euro).
While French euroscepticism may be underestimated, I fear Calbin may be mischaracterizing it. Continental euroscepticism is generally very different from British euroscepticism. Continental euroscepticism is often more along the lines of calling into question how the EU does things and what the EU needs to do, whereas British euroscepticism more often than not questioned EU membership (and the very need for the EU as a whole) itself.
FN initially advocated leaving the euro but dropped then when it proved to be unpopular.
The PVV in the netherlands has consistently campaigned on euroscepticism but only in July 2012 I believe did it clearly and consistently spell out it wanted The Netherlands to leave the EU.
In fact at that point it claimed it was going to be a one-issue party (campaigning on Dutch withdrawal from the EU) between July and the general elections in September. What happened in those elections? Well the PVV lost
a third of their votes from the 2010 election (1.4 million in 2010 down to 950,000 in 2012) in an election which saw a slight
increase in the numbers voting (from 9.44 million in 2010 to 9.46 million 2012). In 2010 by contrast the
PVV manifesto did not outright call for withdrawal from the EU (it hinted at it, by making references to ending the "European superstate"), but rather it called for more Dutch opt-outs in the field of immigration and agriculture and called for a return to the days of the EEC over the EU.
The PVV subsequently regained some support in 2017 in an election which saw a much higher increase in overall voting numbers (to 10.56 million) and which followed on from the refugee crisis affecting the EU.
My take is that even in the Netherlands explicit campaigning for EU withdrawal would garner no more than 10-20% of the vote
at best. So any PVV campaign in such a referendum would face a few hurdles:
1. getting a referendum explicitly on leaving the EU (it would first need other parties in parliament to support such a referendum for it to be enacted (and prior to the 2015 advisory referendum act, good luck getting a referendum to even be offered - without that act even 100,000 signatories clamouring from a referendum won't trigger a process whereby a referendum is done, and even after it is passed the provisions mean that acts already in force generally (such as those which brought the EU into being) are not subject to being put to a referendum. So that would have to wait til a new EU treaty or some EU treaty change and even then it would only be about that treaty change, not membership in the EU itself).
2. Getting public support over 50% for leaving the EU. They could campaign on some tangentially related issue, but even at the height of the migrant crisis they were polling something like 30-35% of the vote. If the vote was on something like EU treaty changes, I
could see the PVV successfully playing spoiler and getting that 50%+1, however the problem then becomes how do you go from the Dutch public rejecting say the proposed changes that introduce the European Stability Mechanism to getting the government
and the majority of the Dutch parliament to take that a mandate to vote for notifying the EU that the Netherlands intends to withdraw?
3. Aside from the 2005 referendum on the European Constitution, the last referendum in the Netherland at that point was in 1805 I believe. 200 years. Maybe they could do a referendum on the Lisbon treaty, but here's the catch - there is no 2015 advisory referendum act at that point, the Lisbon treaty gets ratified in 2009 after being signed in December 2007 and the next Dutch elections happen in 2010. Prior to that the PVV had 9 seats having won 6% of the vote in the 2006 elections. So there isn't really any way for them to actually get to have a referendum even remotely
related to Dutch EU membership prior to 2010.