Arrival in Conques: From the airport of Toulouse, you can go to the train station of Toulouse Matabiau, get a train to Rodez, then take a taki from Rodez to Conques. From the airport of Brive, you can go to the train station of Brive and also get a train to Rodez, then take a taki from Rodez to Conques.
Departure from Cahors: On the end of your trip you can take a train from Cahors. You can also take a regular shuttle bus "Compostela" at the end of your trip to reach a train station or to travel back to the starting point (more information on request).
For timetables and further information check the website of SNCF or rome2rio for all French National trains (SNCF).