Yes and very complicated!!!
- Eurostar to Gare du Nord, Paris
- RER B from Gare du Nord until Denfert-Rochereau and Metro line 6 direction Etoile, descend at Metro Gare Montparnasse, Paris
- Gare Montparnasse, Paris - Daily Sud Express to Lisbon Gare Oriente
- Lisbon Gare Oriente to the Algarve.
Links to the timetables for the last two can be found on my blog here:
http://barlaventostravelblog.blogspot.com Scroll down on the right hand side and you will find a panel entitled - Algarve & Portugal - Travel Transport Links where you will find direct links to the timetables.
