Anything from the US into a regional airport in the summer is going to be pricey, so you may want to make a triangle with open jaw tickets (returning from a different airport). United is running its seasonal non-stop to EDI this year, but those tickets are over £800.
Checking an open-jaw flight for two weeks - IAD-LHR and return CDG-IAD will run about £682 on a mixture of Virgin Atlantic and Air France (gotta call VA) or £750 through Delta (you may need to play with dates to find availability):
https://goo.gl/flights/GkbrEYou can then fly EDI to CDG on Air France for £37-60 each non-stop (note some of these are operated by Hop! which is the low cost AF option, or SqueezyJet):
https://goo.gl/flights/WtFmjAlso note that there are flights from Newcastle direct to Paris for about the same price (£70).
So that would get her to arrive into London on a nonstop flight (none of this stopping in Dublin on a cheaper Aer Lingus on a poorer airline), you can do London and then leave from KX on a proper train (i drop my buddy off on that train once a month - its a very nice Virgin train) without schlepping back out to an airport and she can see some sights on the way up to your town. Then you can fly to Paris and she can fly home from there (on a very nice A380 AF flight with extra legroom). All (for her) for about £850 or so. Not bad for June in two heavily touristed countries.
For you to get down to LHR to pick her up - check out Flybe for decent fares from EDI, otherwise there are internal BA flights direct. Don't be afraid to look for a one-way!
Also, I would suggest booking trains as soon as you know your dates - they can be heaving with Asian tourists going to York and Edinburgh, especially in summer.
One last thing - checking all DC airports to EDI direct in June is turning up WOW air (transfer through Iceland - they are fine but no frills, like flying Spirit longhaul, in a single aisle aircraft, from Baltimore), or Aer Lingus and Stobart Air via Dublin for about £500.