[…] I guess that I should be more regular.

Your guess is correct. I’m glad you’ve provided so much info, as unfortunately skincare is still something that has the stigma of being “unmanly” and just for females while actually anyone can profit from it.

Since you have very dry skin which probably ranks high on sensitivity (reasons being: past troubles with dermatitis, possible contact allergy with menthol judging from one of our past conversations), you’re doing really good with the moisturising soap. For cleaning, I’d recommend something mild with moisturising ingredients like glycerine, squalane and urea, but it sounds like you already got that in check 👍🏻
As for moisturizer: dry skin can really benefit from it the most. I’d suggest a product with little to no alcohol as it further dries out your skin (the further down any alcohol is in the INCI, the better for your skin type). Avoid menthol and essential oils too due to your past history of dermatitis. I’d recommend something with jojoba oil, glycerine, hyaluronic acid, ceramides. These ingredients work well with dry skin. Unfortunately, since your skin is very dry, this also means that you should avoid aftershaves with alcohol in the dry months (autumn and winter). I’d recommend a witch hazel toner, perhaps with aloe vera too if you can find one.

Due to my research, I found out that the concept of a drugstore is completely foreign to France and you basically have to rely on supermarkets for cheaper creams or apothecaries/pharmacies for the €xpensive+ stuff (Avené, La Roche-Posay, etc.). Since your skin seems to be very prone to irritation, I’d also recommend a repair balm for patches that struggle with redness and itching. Comptoirs et Compagnies has balms with manuka honey, which helps with inflammation due to its antibacterial and regenerative abilities. Of course, any product with low or no alcohol and perfume would work well. I’d also recommend a broad-spectrum SPF product for skin cancer prevention and anti-aging, due to your dry skin you can actually take one of the “richer” products (not in price, but those rich in skin food oils like jojoba, argan, castor or almond oil).

I hope I can help you with these tips in any way; don’t be afraid to ask further questions! 😉
I personally still test different products for the needs of my skin, but I already have made some sizable progress. You’ve inspired me to write more about skincare, as I personally feel it goes well with traditional wetshaving and its self-care aspect.