I have visited Pic du Midi, but I took the hard route and went up there by bike! (The Col du Tourmalet is a classic Tour and Vuelta climb :-).
You’ll need to get the bus to La Mongie to visit, as this is where the cable car goes from. I think (in normal times) there is a bus from Lourdes or Tarbes to La Mongie, which may suit you as both have SNCF stations. There was talk in summer 2020 about the French Government reintroducing the Paris-Tarbes sleeper service, but this might not happen quite yet, and there is (again in normal times) still the Paris-Toulouse sleeper, and Toulouse-Tarbes/Lourdes via train is a couple of hours.
There is also the Cité de l’Espace in Toulouse which I can recommend as well.