I thought maybe one of the horse owners on here might have contributed by now, but as no-one has replied, apart from your choice of vehicle, there are general rules for towing trailers in France which you should consider.
First, all trailers with a laden weight (PTAC) over 500kg must be registered, so must have a Carte Grise, and for this they must be homologated in the EU.
Homologation documents are provided by the manufacturer, and may sometimes be obtained retrospectively, but take care when buying second hand.
PV = poids vide, PTAC = poids total autorisé en charge, PTRA = poids total roulant autorisé
A trailer with a PTAC over the specified value may not be towed if the conditions are not met even if it is empty.
On some great and glorious day the plain folks of the land will reach their heart's desire at last, and the White House will be adorned by a downright moron.
H. L. Mencken 1880 - 1956
Some may not like his views, but what a prediction!