I was fortunate enough to be staying close by to the Bois de Boulogne- a huge park just West of the city. It was a former forest designated as a royal hunting ground that is currently more than twice the size of Central Park. Because of it's size and relative isolation, it's become a bit of a red-light district, with prostitutes hanging around at all hours in the open.
It was a lovely park despite some sketchy isolated areas. There were lots of dog walkers and Parisians enjoying the gorgeous autumn weather.
There are two livery stables where you can ride horses through the park, plus Longchamps Racecourse is in the south end...so watching your step on some of these paths was a priority. It really seemed much further out of Paris than it was...every once in a while, I could glimpse the top of the Eiffel Tower just beyond the tree tops.