It depends. (As all things do.) I'm personally of the opinion that this will not result in any major long-run changes in the value of the Euro. This will, however, negatively affect the pound.
Most of the currency volatility that we're currently seeing is a result from investor panic rather than actual changes in economics. The UK and EU still need to discuss exactly how the UK will leave before investors can accurately assess the economic impact.
Brexit will negatively impact the EU by:
- Decreasing the amount of trade between the EU and UK, due to
increased trade barriers (this is going to affect the UK more than
EU, mostly due to size)
- Increased instability from political changes; may result in a domino effect on other troubled Eurozone countries attempting to
leave (see: Greece)
- Lack of job opportunities; the UK has a lot of foreign workers who will eventually have to go back to Europe when their
Brexit will positively impact the EU by:
- Forcing a possible move of the financial industry to European
centers rather than London
In my opinion, this currency change has more to do with a shift in politics than economics. The UK and EU will probably agree to some form of trade policy that will mitigate most of the economic damage.