Jogging and running itineraries : Thanks to my children, I can share some nice itineraries around the apartment
swimming pool: you have a large Public swimming pool 5- minute walk from the apartment in les Halles
gyms: I can share a list from posh to cheap and you could buy a pass for 1 or more sessions
You could visit all of Paris around a park and garden theme!
On each side of Paris limit, the Bois de Vincennes and Bois de Boulogne.
Parc Monceau, Parc Montsouris, Parc de La Villette, Parc André Citroën.
Just to name a few. I can share you lists and maps.
Gardens: little gardens are spread all over the City. Some secluded. When weather is warm enough, it is a good plan to buy a nice eating out lunch, and enjoy on a bench, taking advantage of a quiet atmosphere or watching the crowds.
I am happy to sahre with you my picnic tips and some garden addresses wherever you'd like to stroll