The French, being an nation of rational and orderly souls, have an excellent system to regulate both tourism and the sport of equestrianism. There is a detailed, graduated system of qualification for riders and guides and rules about running a riding business. So, basically, you can be confident that horses and horsemanship and the service on offer are all of good quality.
The entire country is criss-crossed by riding trails. Each region has a committee to promote equestrian tourism. As a hugely popular sport, there are riding stables all over the place. There is a strong tradition of competitive endurance riding right down to a short couple of hours hacking for leisure and pleasure.
Be very clear and honest about your abilities because there can be assumptions made: I had not met a French ‘trekking saddle’ until riding in Cathar Country and so did not sort out the rigging until about the third day. Of course, I should have asked! Really good saddles, by the way.
Just be aware that it will be faster than most American riders are used to. A canter means just that, not a four beat shuffle. A gallop means going fast enough to bring tears to your eyes, not a polite ‘hand gallop’. A walk aims to get to lunch before the cafe closes. They will ride up and down and over and through and it is all great fun!
A hack is usually a ‘promenade’ or a ‘ballade’, a pleasant couple or few days from point A back to point A is usually a ‘randonee’. A ‘raid’ by contrast is very fast, all day.
The department around Paris is ‘Isle de France’ (use your translation tool and get the gist or use the English version of the website you look at)
http://www.seine-et-marne.fr/randonnees-equestres
http://www.loisirs.fr/Ile-de-France/Randonnee-a-Cheval.html