Northern France can be quite chilly! Note that jeans are not very good thermally. In summer they are too hot, and in winter they don't keep you very warm. Whatever the locals are wearing for winter, you'll need better. Good quality clothing does not always equate to the best insulating clothes, and cheap clothing is unlikely to serve you well.
I suggest you visit an outdoor shop and obtain advice on thermal base layers. For mid layers fleece (it is not sheep's wool) is the modern fabric. For outer layers a windproof layer is needed, preferably a 'breathable' one. This can all be quite expensive but unbranded clothes are good if you choose advisedly. Outdoor shops usually sell at a range of price points.
I like to wear a thin vest or shirt layer between the insulating layers. This fabric itself might not have much thermal property, but separating two thermal layers improves the performance of both.
But above all, you somehow have to convince your body that it needs to generate heat. Anecdotally, an expatriate friend brought his family to live in UK. Their home climate was equatorial, at an altitude that is comfortable all year round. But their bodies had no practice in generating heat in cold weather. They suffered badly and returned home after two winters.
On a local scale I too have this problem worse as each winter approaches and somehow I have to accustom my body to generate heat. I'm not sure if there is any way to teach this, but one technique is to let yourself really feel the cold, and let your body respond. As with anything, if your body isn't used to it, you have to practice it.
Here is an example. It is snowing and you go out for a snowball fight. Soon, your bare hands begin to go numb from cold. But after a while, your body responds and sends more blood to your hands, and before long they are vibrant with warmth. Activity can be the key to this. If you are moving, your muscles generate heat.
In an emergency situation you begin to shiver, and that activity generates heat, but it is a warning that you need to take some quick action to warm up by other means. But unless you are in an extreme environment, tired or hungry; if you can relax at this point and let your body work to generate heat, from your inner resources, instead of fighting it, you'll have made progress.