I just found out where was the problem ! Actually I checked the WhatsApp Q&A, and it explains well that sometimes this bug comes from the APN connection.
Therefore you need to go to Parameters - Mobile Networks - APN (Access Point Name) - Full Internet SRR
There are several options offered, just make sure the “Full Internet SRR” is ticked. In my case, the “GPRS SRR” was ticked instead.
Now it works perfectly !
Many thanks to my dear partner, who brilliantly found the trick ! 
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