Hi Disneyfan,
I guess that this is no problem to look for the "Paris Ring" caches using only metro and RER... All of them are within the 5 zones range anyway.
I assume that the "Paris Ring" originator (Intothewoods) made the caches available only using the public transportations.
Some of the "Paris Ring" refer to metro/RER access in the description.
Of course, all of the Paris downtown caches are accessible as well without specific transportation way.
Enjoy your trip.
Pat - DarkVaduke