Arrival in Cahors: From Toulouse airport (Blagnac) to Toulouse train station (Matabiau), you can take a shuttle bus. Then take a train which goes directly to Cahors. From Paris, you can get from Charles De Gaulle airport to Gare Paris Austerlitz using the RER. Then, there is a direct connection from Paris Austerlitz to Cahors.
Departure from Lectoure: At the end of your trip, there is a public bus which leaves from Lectoure to Agen, once every 4 hours. The bus drive takes an hour. From the train station of Agen you can easily reach Cahors or Toulouse.
For timetables and further information check the website of SNCF or rome2rio for all French National trains (SNCF).