Good news: In Paris, the rules for tourists have become softer.
The rules in the nearby parks have always been fairly tight. Only in 77 of the 490 of them are bicycles, ball games, and picnics permitted. Now, both locals and visitors are free to do this practically anywhere. However, there are still some parks where all you can do is read a book while sitting on a bench. Ask the locals about the rules when you are in particular parks if you plan to visit Paris.