Bonjour
@Anne&Pat For info - you may be able to achieve what you're looking for through a combination.
La Malle Postale operates between Le Puy en Velay and Lectoure. They offer a service that allows you to leave your suitcase in their office in Le Puy and, when you are getting near to e.g. Lectoure, you notify them (with some days' notice I guess) and they will have your luggage there (at your accommodation) to meet you.
we store your luggage safe during your hike
From Lectoure to SJPP, another service
may offer the same thing, but you'd need to check.
For example,
Transport Claudine does day to day baggage transfer from Conques through to SJPP. Perhaps they also offer a similar service to La Malle Postale and could take your luggage through to SJPP to arrive there on your same day arrival.
Transports Claudine-Compostelle-Vallée du Celé-Transports de bagages et personnes d'étape à étape-Transfert véhicules
Both La Malle Postale and Transport Claudine have good reputations, as far as I know. I think there are a few more baggage transport companies that go through to SJPP, but I am not familiar with them.
All the best. The Le Puy Way is wonderful.