I don't live in France, but i come regularly to shop cosmetics that are not possible to get in Poland.
I would highly recommend:
Dessange lisse absolu richesse
baume demelant
lissage integral et protection

After becoming CG, that is my only hair cosmetic, from what i had in my bathroom, i can use in low dew points (it has some humectants, but quite far). And believe me - i'm a BIG product junkie, so i had a lot of choice in my bathroom I use it as a co-wash and my hair loves it! Moisturizing is turned on Also my hair are more shiny.

Ingredients: aqua, cetearyl alcohol, elaeis guinessis oil (palm oil), behentremonium chloride, steamidopropyl dimethylamine, argania spinosa oil, linalool, glycerin, limonene, chlorhexidine dihydrochloride, xylose, citric acid, citronellol, hexyl cinnamal, buthylphenyl methylpropional, parfum

About the price I remeber it wasn't expensive nor the cheapest - somehow in the middle closer to the low cost (I use different currency, so sorry for not being precise).

(still learning how to upload an avatar and write subs)
3a, high porosity, normal density, medium texture
because of results in snap test needs moisture AND proteins

Co-wash: Dissange lisse absolu baume demelant
CO: looking for humectant free nearby, Dissange^
LI: coconut oil/ monoi
Styling: looking for sth humectant free nearby