About the discovery of my arduino on my modem router

I am using one Arduino Uno + Ethernet shield 1 from 2011 and recently one Arduino Mega + shield2 and in both case with IP address fixed, the problem (or anomaly?) is that these two devices are not identified by my modem router (= a LiveBox Orange), despite the fact that locally everything fine but I cannot remotely have a connection via my modem router as the 2 Arduinos are like a "phatom" ! So the shield 2 did not solve this problem. Is it a soft problem ? In it I put the fixed IP address and the Mac address of the shield. I wonder if someone has the same anomaly!

you.

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