The three paths
A thermostat stuck open sends coolant to the radiator too soon, so the engine struggles to reach running temperature (often around 85–95 °C, not a universal number).
If the radiator is already hot to the touch and the needle is still on the floor, the engine may be fine and the display wrong. Some cars have two sensors.
Very short winter trips may never let the engine settle. That is wear and extra fuel, not always a broken part.
What to compare
Cold engine, level between min and max. After a few minutes idling, the top hose should stay only warm while the thermostat is shut. If it is burning after two or three minutes, the thermostat may be open.
OBD at ~90 °C and a needle on the floor → gauge/sensor. OBD and needle both low on the road → thermostat or over-cooling.
Translation of the live French article. Not a diagnosis. Service intervals stay with the manufacturer.