My brother and I are planning a trip to Europe from the US late summer/early fall. I have Southwest airline points, and we are probably going all around Europe so specific airports and times are not really important. What is the best way to search for the most economical flights?
There is no generic solution, you have to try around various option. Google flights (https://www.google.com/flights/) or ita (http://matrix.itasoftware.com/) do not allow to search across multiple start countries at the same time, but you can for example enter JFK or MCO to 'MUC', and then add all airports within 3000 miles of MUC (that's Munich). This will show you some cheap options all across Europe.
You can buy any flight with Southwest points, but only at an inefficient rate. Still, better than not being able to use them.
[currently MCO-CDG with Norwegian is ~250$ roundtrip, on the right weekdays, for example]