Sadly, most across Europe rail fares can not match the current 'Easyjet' type air fares. You need quite a lot of experience to get a 'cheap' rail fare across Europe. For future reference, I find the most economical way is to book in sections and a long way in advance (best fares only available the first day of sale - usually three months in advance) and for anything involving France book via SNCF's own website rather than Rail Europe.
But all the above is pretty hard work even for me!
Having said the above the obvious route to Alicante is overnight hotel talgo Paris - Barcelona and Renfe express Barcelona - Alicante, which probably only means two separate web bookings, but...
