What do you advise me to bring in my suitcase for my stay?

You can refer to the page « What to put in your suitcase »
Bring a flashlight. Power cuts are frequent. Also take a windbreaker and a small jacket with you if you plan on climbing. A small first aid kit can be useful; disinfectant, blister bandage, gauze, waterproofs bandage. You will find them in supermarkets or pharmacies all ready in France.