I am sure that you can get a train to Perpignan from Narbonne. Try http://www.sncf.fr for details. A taxi will cost you an arm and a leg ... and if you need a taxi back from your event, you might not get one if there are too many others who want to use them. They might not take you (if they are in a contrary mood) because Narbonne is not in the Perpignan town boundary - which can be the limit of their licence.

A site like http://www.viaMichelin.fr will help you calculate the actual distance between the two points you need.