It will be difficult but not impossible. The mayor of the commune where your property is located has to be first contacted and convinced, and thisiwil also depend on how far other habitations are located, noise, etc.
If he is convinced ,and is prepared to give in writing a non-objection letter, then it is worth starting the process. I believe the Direction de l' Amenagement du territoire has also something to say before but the mayor should be able to tell you this.
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You can start, as suggested , by looking at the fna website. they have a good link to french internet sites site .try the DGAC one and ask the question there . they have also an own Forum and you can also try to ask there if someone has stated the process of operating its own field.
Good luck and keep us informed of the results.
the fna web site is :
www.fna.asso.fr/fna/
(please, do not put "le" after the asso on the address )