The RCC doesn't own Notre Dam if course. Not sure they own any f the churches in France either, could be wrong though.
Churches were taken into State ownership during the Revolution and have so remained - although I do not know of the status of any churches built since then.
The three churches in my commune are all owned and managed by the commune. There is an individual responsible for managing bookings. The church in the main village is used for both RC and CofE services (local expat community). It accommodates more Anglican than RC events.
I note Alan Burns vacuous comment. He clearly fails to understand the cultural importance of ancient churches if he perceives them to be of interest only to believers and grockles. The buildings encapsulate a huge range of important cultural attributes related to the development of modern values - one of which is religious belief.