Q: I can't find a bus or train that goes from Barcelona and that stops at Pau (France). Can you kindly inform me if there is any connection?
A: Your question is to do with a destination outside of Barcelona and therefore we cannot answer fully however we can point you to these resources to help you find your own answers:
Take a look at the official website of the Spanish Railway Company, RENFE. There you can look up your train itinerary in the English version introducing "Barcelona" under origin and "Montpellier" under destination. In Perpignan you would have to change the train and take a French train to Pau because there is no direct train leaving from Barcelona.
You can also check the information regarding the França Station in Barcelona. The Estació de França , as it is called in Catalan, is the Railway station where the trains to or from France leave or arrive. To exactly know its location, nearest Metro station, connection to the airport, please follow the link below.
Regarding the bus connections, you can visit the official website of the Estació Barcelona Nord, the bus station, to see which companies travel to France, to where and on which days they are available.