There is no such thing as a "Eurorail train." If you mean that you have been looking at Rail Europe to find trains, stop immediately. They are a reseller, they do not list all trains, and they often mark up the tickets they do sell (sometimes substantially).
To find train schedules for almost all of Europe, use the Bahn (German Rail) website http://reiseauskunft.bahn.de/bin/query.exe/en, following Rick's tutorial: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules
This website will not list prices for trains that do not start or end in Germany. To get prices, use French Rail (who actually operate the trains on this route): http://en.voyages-sncf.com/en/. Choose "France" as your ticket collection country. Check prices for tomorrow and for your travel dates. If there's no difference, no need to book in advance. If there is a difference, you can try booking on that website, but some have had difficulty. If SNCF's website doesn't work, people report better success with Capitaine Train (same prices as SNCF): https://www.capitainetrain.com/
And be careful with spelling; it's St. Jean Pied de Port, not Pier. Not all websites are as forgiving of misspellings as Google (with its handy "did you mean?" feature), and that may be why you didn't find the train.