Michael,
I am a German long-distance hiker who has done the Triple Crown in the US – so I know the American and the European side of the hiking world.
Basically you have almost endless hiking opportunities in Europe by piecing together your own route. But keep in mind that there is no "thruhiking community" like in the US. Long-distance pathes are usually restricted to one country only and because European countries are smaller than the US those trails are shorter.
All the suggestions so far are in a more or less alpine area. If this is what you want to do, go for it. But if you decide to go for the Alps or Pyrenees keep in mind that you will not encounter pristine wilderness like in the US but devolopped mountains with ski lifts and cattle with cow bells everywhere.
The trails/hikes suggested so far are the very popular and obvious ones but I want to suggest at least one other that might be interesting for your girl friend:
http://www.salzburger-almenweg.at/en-index.shtml
This really scenic 350 km trail has been created only some years ago and is very easily accessible by public transport. As an added bonus to alpine scenery on this trail you will walk from Alm to Alm. An Alm is a mountain hut for people tending to cattle that is grazing in the mountains in summer. You can usually stay very cheaply overnight in those rustic huts and buy local produce like butter and cheese made directly there. You will have a great cultural experience.
But in regard to your girl friend I would suggest hiking in a non-alpine environment. I have just myself finished a 1,200 km hike through Germany and the British 2,000 km classic hike through the UK from John O'Groats to Land's End. You can find a trip report with photos and details for trip planning on my English blog:
Germany: http://christine-on-big-trip.blogspot.com/search/label/German%20hikes
UK: http://christine-on-big-trip.blogspot.com/search/label/JoGLE
If you are interested in either one please let me know and I could send you the relevant gpx track or help you with any other questions.
Also keep in mind that July will be awfully hot in Turkey and Greece and therefore not suitable for hiking the Lycian or St Pauls Way.
Christine