Currently living and riding in France and I have to say the internet is your best bet here. Paris is in the Ile de France region so you’ll have more luck searching under Ile de France as there aren’t a lot (or any) of stables in the city itself.
Other key words: centre equestre (equestrian center), randonnee, haras, balade a cheval.
I also found these: http://www.balade-cheval-chantilly.com/
http://www.chevalnature78.fr/
You could also look into booking through a tourist agency, there are a ton: http://www.rideinfrance.com/
I wouldn’t count on having a lesson or riding out alone - think a nice country hack would fit this situation best. And I have to say I’ve been a bit disappointed with the level of training over here, but never with the quality of a nice hack! I agree, they do love to galop fast but that should be no problem for you.
Usually if you see ‘club du poney’ it is a center for children (there are probably 10 for every other riding situation). Centre equestre or haras would be more your alley.
PM me if you need translation help or have more questions, it took me two years to figure out this stuff so I’m more than happy to share the knowledge 