Ryanair.com starts operating direct flights from Paris Beauvais to Faro, Airport 4 times a week from April 2010.
Unfortunately, Easyjet's flights from Orly appear only to start from 1st July or so. (To be confirmed.)
You best bet for Barcelona, would be either by Ryanair.com from Faro to Madrid and then train/plane to Barcelona. Alternatively, as you propose fly to Lisbon, pick up a car, travel to Lagos and then back to Lisbon.
There is no direct train link from Faro into Spain.
