i don't know french law but what i know from similar situations in the UK where livery yards sometimes get stuck with the same situation is this :-
simply put she has a contract with you, even if not on paper, if you have a paper contract fine, if not did you put an advert up/posted etc anywhere & if so do you or can you get a copy of it, if so this copy forms the basis of a verbal contract which she agreed to.
now assuming some sort of contract which she has defaulted on then after 'a reasonable length of time'
(taken as the length of time a reasonable person would expect to wait,- but not actually fixed in law- usually 1 month after failure to comply with terms etc)
you are within rights to issue her with notice - registered letter.notieres letter whatever - of intent to furthur action if she does not pay/do whatever within same reasonable period, but this time state it as within 1 month from../../....
declare to her what the action will be....
usually it is the intention to sell the property (her horse) & take payment & any costs due including costs of selling such as agents fees or auction transport etc from any money obtained, & by law you have to forward any left over to her so you need to know where she wants it sent.
Note 1- if she does not tell you where to send her 'change' you can put it in an account/jamjar whatever & keep the interest forever, it's not up to you to find her to pay her.
note 2- the price paid if not at public sale has to reflect the real value of the horse, no selling a champion to a mate for a quid is allowed.
state on the letter that if she does not contact you with payment or other terms of offer by the stated date then you will assume she has voided all ownership of the property (horse) which you will now dispose of (in a monetary sense we hope!) as stated above.
if in fact the amount owed to you is about what the mare is worth & you are prepared to swallow it and choose to give her away thats ok too.
if you have a mairee or a local notiere i would go see them, they may be able to help and the notiere is p'haps the person best able to word this sort of thing, any cost he charges will come out of the mares sale or can be added to the owners bill to pay.
i am told there is a system of small claims court in france, again ask the mairee or notiere about it.
i have used a similar format in the UK on solicitors advice with a human tennant who left owing rent and the house full of his furniture, after the old reasonable time & due notice waffle we sold the funiture to cover costs, inc cost of solicitor & removal to the auction & sent him the change to his Mums address, so in Uk law it is deffo an OK way to go about this.
good luck, bye