Arriving at the lowest terrace I discovered a number of tourists waiting for a tour of the ‘Grotto’ cave system (Grotte de l’Observatoire), which is guided and runs on the hour most hours through the day. The limestone caves were discovered in 1947 by a team building the gardens. The system was opened to the public in 1950.
When I arrived at the entrance on the lowest terrace of les Jardins, it was a) hot and b) 2 minutes before the hour, so I chose to join the free tour. The guide warned that there were a total of 600 steps down and up, some slippery, and temperature was a constant 18C down in the caves 65m below us, while it was about 27C outside.
Claustrophobia can be a problem for some when underground but these spectacular limestone caves are large and well-lit so unlikely to trigger issues in all but the most sensitive. It is a brilliant walk, the tour was fantastic, the caves were extensive and stalactite/stalagmite formations weird and wonderful.