That's picture looks like a Nest 3rd gen, although it doesn't appear to say Nest on the Heat link button. Maybe you have something different in France / Luxembourg?
If it is a Nest 3rd gen, in the UK, the wiring terminals are normally as below.
If yours is the same as above, the two wires in your existing thermostat go to terminals 2 'heating common' (brown wire) and 3 'heating call for heat' (black wire)
Your old thermostat is battery powered, but the Nest Heat link is mains powered, so it also needs a 230V supply connecting to the N & L terminals. This should come from the same electrical connection that also supplies the boiler.
If you are planning to connect the Nest thermostat to the T1 & T2 terminals to provide it with 12v (instead of a separate plug in power supply) then you will also need to provide an earth connection to the earth terminal.
If you have something different, post back details of the wiring terminals.