Good idea. Haven't been there since 2010 but it was very dismal then. Was very glad I was staying with friends in Forest - an odd borough - or commune? - as it has areas as dismal as Gare de Midi, quite upscale areas uphill and a pleasant middling area, where I was staying. I assume the places whatagain recommends to look are handy via public transport to the Gare du Midi.
Have you figured out whether your bargain fare was a ticket or a reservation? Sounds like a lovely trip - I love train travel.