I recommend holding on to your bag until you arrive at your starting place. Then, access the local post office (La Poste) to send the bag as a parcel. If you are sending from one French place to another French place. This is the most economical method IMHO.
As you have already obtained the agreement of the recipient, this is easy-peasy. Get a tracking number, and have the name address phone and e-mail of the recipient. They will ask for all of that when you send it.
La Poste has an free app available for Android and Apple on the respective websites. Use this to track your bag. Also, ask the recipient to tell you when he / she receives your bag. Knowing that your bag arrived allays a LOT of anxiety.
If sending across a national frontier, using the post office does not work as well, as all cross border shipments are considered international, even between EU states. this interjects more time, complexity, and cost. Some, including me have had problems shipping things from one country to another using the national postal systems.
However, sending wholly from and two a place wholly within one country, use that country's national post system. The Spanish el Correos works great, as does the CTT (Portugal) for in-country point-to-point. I presume France's system, will work as well.
Hope this helps.