I love Paris. It's not particularly well-served by cheap flights but easyJet can get you to either Orly or CDG from Belfast, Bristol, Edinburgh, Liverpool, Luton or Newcastle.
However, for me, one of the joys of visiting Paris is travelling by Eurostar (from �29.50 each way, from St Pancras, Ebbsfleet or Ashford).
Once you get there,travelling around is cheap and easy, using the RER trains and the Metro (or the buses if you're not in a hurry):
http://www.ratp.info/informer/anglais/paris_vi site.php
Paris has a reputation for being very expensive but you can still have fun (and eat well) on a budget. For cheap accommodation, try this website:
http://www.hostelworld.com/
(Don't be put off by the word 'hostel' in the URL. Just use the 'Additional search options' to look for guesthouses and budget hotels).
For cheap (but lovely) food, head to the Latin Quarter. (Take an RER train, on Line B or C, to St-Michel Notre-Dame). There are loads of restaurants which will serve you a 3-course meal from around �10.
One of the best ways to see Paris is from the river. Some of the guided tours cost 'an arm and a leg' but the regular river bus service, Batobus, is much more reasonably priced. The service runs between Notre Dame cathedral and the Eiffel Tower, with stops at several major tourist attractions en route. A ticket is valid for unlimited travel for a whole day, so you just hop on and off as you please:
http://www.batobus.com/english/8escale.htm
Chris