Where is Manosque? Is it anywhere near Paris? There's a top hormone doc in Paris.
I live in the Oise, and there's no-one round me that knows anything about thyroid, so I self-treat.
NDT is illegal in France, as is HGH - but you'll probably never find out if you need that because they don't test for it!
However, you can get T3. Some doctors will prescribe it, some won't. But try asking for it. Ask for Cynomel. You might strike Lucky.
As others have said, your Frees are far too low, and your TSH is too high. Your iron is too low - which will make it difficult for you to convert - and your B12 could be higher. Try supplementing with some form of iron - Solgar's gentle iron, perhaps - and Jarrows sub-lingual Methylcobalamin, you can get them on Amazon, saves battling with pharmacists who are likely to demand to know why you want them! lol
Doctors and endos in France, in general, are very much like doctors and endos in England. In general, they know nothing about thyroid, and even less about vitamins and minerals. You might strike Lucky, but go prepared to be disappointed. How is your French? It can be difficult when you're struggling with the language. But there are several of us here who live in France, so there's always help to be had, be it with the language or the blood results, or anything else. You are not alone!
How you know if you should increase or decrease is like this... TSH should be near the bottom of the range once you are on thyroid hormone replacement. So, if it's over one, you need an increase. FT4 should be in the top 75% of the range, so if it's below mid-range, you need to increase your dose. FT3 should be up near the top of the range - some people even need it slightly over. So, if it's lower, and you're feeling bad, your dose needs increasing. If your FT4 is higher in its range than the FT3 in its, then you aren't converting properly, so you need some T3 (Cynomel).
So, how does that work out for you? The FT4 is just slightly over mid-range (mid-range being 8.65. The FT3 is a good way below mid-range (mid-range being 3.4). So, a) you're not taking enough T4 and b) you're not converting. That could be due to the low iron, but some Cynomel would be a good thing, anyway.
Vitamin B12 shoud be at least 600, but better up the top of the range. You can't over-dose with B12 because it's water soluable. But if you supplement, take a B complex with it, because they all work together. And that will bring your folate level up. But make sure you get a complex with methylfolate rather than folic acid.
Ferritin should be at least mid-range. You also need to get your vit D tested because that is usually low in hypos. As is magnesium, but I doubt you'll get that tested. Just try taking some and see how you feel.
You might want to add a bit more salt to your diet, because the adrenals need fat. And you want your adrenals to stay strong because you need them to be able to use the thyroid hormone you're taking. Also take lots of vitamin C. It helps you to absorb the T4 you're taking, and is essential to take with iron if you want to absorb it and not become constipated! And the adrenals need it too.
As to the other hormones, if your endo won't test them, see a gynecologist, she might be amenable to testing your sex hormones.
May I ask which French forum you went on? There are some dreadful French ones with people giving terrible advice! The only decent one I knew has disappeared.
Well, hope that's helped and is not too much info in one go. Good luck with your new endo!