Importing an equine into France from Spain is much the same as importing into France from the UK, except this route is not part of the Tripartite Agreement. This means that equines moving between France and Spain will need, in addition to their passport, an EU health certificate and export certificate issued by a vet.

If an equine is exported from Spain into France permanently and not just passing through, they must have their passport over-stamped by the Haras Nationaux.

All pure bred Spanish horses (PRE) worldwide  are registered in the Spanish State Studbook which is administered in spain by ANCEE-LG. The registering of PRE horses is strictly regulated no matter what country they were born in. There is some excellent information on Spanish horse papers here.

PRE horses imported into France from Spain may be entered into the Registre Français du cheval de Pure Race Espagnole held by the Haras Nationaux.

If you are moving permanently to Spain with your equines remember you will need to register them in the province in which you will be living.