Other side You need to connect into PE (ground) from Your installation (most likely from wall socket).
Would you know if there is any kind of adapter that allows one to insert the earth lead into the ground of an EU/French outlet? The earth on an French outlet is a male pin, so there's no way of them connecting without some sort of adapter.
This won't earn any safety certificates, but it works:
(Attachment Link)
BTW is that a metal dust that went into socket? In that case You should change that socket into at least
IP44 (better protection from dust and water than IP20 which You have on this photo) - in easiest words, it's a socket with a cover on hinges.
Otherwise it can compromise connection (fire in case of more current like couple ampers literally - don't ask me how I know) and since it's metal, it can accumulate inside and behave like overpowered heater, which also can cause fire to start.
Example IP44 socket looks like this: