In the absence of any specified definition within the legislation, it is usual to take the normal meaning of words at face value.
Therefore; A ‘private’ visit is one which is not undertaken for business purposes.
So, my son comes from the UK to visit me at my home in France simply because he has not seen me for quite a while. We are related and so this would be a ‘familial’ visit.
On the other hand, if my son comes to visit a mate of his who lives permanently in France, then this would be a visit which is ‘privé’ as the two of them are not family related.
However, if my son comes with his girlfriend to show her the sights of France while travelling around the country, then the visit is ‘touristique’, not least because while it is neither ‘familial’ or ‘privé’ it has to be something.
Often it is just as much a matter of what something isn’t, as opposed to what it is, when interpreting and applying legal texts to practical situations.
I think that Article L313-2 is the part that really shows the intention of the legislation, in that it makes plain that the person applying for the A d’A is taking responsibility for the financial liabilities of the visitor in the event that the visitor is unable to personally discharge them.
Therefore I believe that the spirit and intent of the legislation is to keep out the riff-raff who may become a financial liability to the Gov’t of the host country. A visitor who is in possession of a return ticket, plus a valid bank or credit card is not going to be turned away. After all, it would not go down so well with the French Tourist Ministry, or indeed the Finance Ministry who are no doubt both very keen to welcome foreigners who have money to spend.