Both players arrive on free transfers after contracts at their previous clubs were cancelled by mutual consent.
Former Wales Under-19 player James, 20, played in one Bluebirds game, as a late substitute in a 2014 top-flight match.
Goodship, 22, spent the second half of last season on loan at Huish Park, before a loan spell at non-league Braintree Town earlier this term.
He did not make a senior first-team appearance for the Cherries, but did previously score once in 10 league matches for Yeovil.
The Glovers are 16th in the table, nine points below the play-off places and nine points above the relegation zone.