EasyJet fly from Newcastle to Paris (Charles de Gaulle).
I've just checked some random dates in July and I was offered a return fare of �69.71 (including taxes and charges but excluding the travel insurance which easyJet automatically offers you). There might be cheaper fares available if you hunt around the easyJet website.
To get from Edinburgh to Newcastle would cost you �40.20 if you simply turn up at the station and buy a Saver return but I've taken a look at the National Rail website and (for the random dates which I've checked) there seem to be plenty of advance purchase tickets currently available for just �9.50 each way.
To get from Newcastle city centre to the airport, take bus no 75/76/77/79 from Eldon Square. (I doubt that the fares would be particularly expensive).
So train, bus and plane should come to under �100 in total.
Easyjet website:
http://www.easyjet.com/en/book/index.asp
National Rail:
http://www.nationalrail.co.uk/
Bus journey planner here:
http://217.23.229.206/jpclient.exe?newQuery=ne wQuery
Chris