I love you guys, another great thread. We exclusively use carbon steel fry pans. (Easier to find here, lighter because they are thinner, and more responsive) We have a De Buyer dealer nearby, so they have been my preferred option.
In fact I just bought a couple of new ones last month, a very thin 1mm, paella pan and a thinker flat bottom wok type pan. I actually use the paella pan as an oven pan mostly my wife hates the oven getting too messy and this has made it super simple.
Anyway, I was really unsure how that thin 1mm steel would take a season but seriously it was very easy. Most people tend to use too much heat and overcook the oil. I used flaxseed oil, but honestly olive oil is just fine as well. Heck I've made it work with coconut oil, which is against all the rules.
IME the key is being patient the first uses. First season is, clean the pan, heat it on the stove top, or if you need to coat the whole pan then use a hot oven. 250 deg C is fine IME or med-high on stove top.
When the pan's hot, pour a small dollop of oil and wipe it around the entire surface of the pan, first time, keep it under heat 5-10 min, but not to the point it smokes.
Then take it off the heat, and wipe the excess oil off right away!
From then, every time you use the pan is a mini-seasoning, and how you take care of the pan post cooking is the main thing, never use soap unit the pan has a serious black crust built up. Getting the crust takes some time, but it will cook fine without it.
Just use plastic fibre dish brush, and for anything that sticks and wooden spatula or similar. The brush we have has a plastic scraper built in, that works great.
After cleaning, dry the pan immediately! Then pour a small dollop of oil in the pan and wipe it around, cleaning off any excess. For me, this post treatment has been critical, and it also help avoid any rusting. Some go as far as reheating the pan in the post treatment, but I don't find I need to do that.
I'll try to post some pics soon.