Don't know where Wise Owl got that Bala is an alternative name for Basel. I'm Swiss, my father was from Basel, used to visit my grand-mother there when I was a kid, and never heard of Bala.
What I think you're referring to is Bâle, which is the French word for Basel. But it's not a connection, it's your final destination.
Here is the exact itinerary (in reverse, from Switzerland to Paris) :Zurich–Bâle–Mulhouse–Belfort–Dijon–Pari... Gare-de-Lyon
UPDATE: Christiane: Go to either www.google.fr (France) or www.google.ch (Switzerland) and type in Bala. I defy you to find even one credible reference linking this word to Basle. There is no city/town/village/hamlet in France or Switzerland named "Bala" much less on the rail line between Paris and Basel. There is a village in Roumania and Turkey called Bala. Un point, c'est tout! Das ist klar!