The problem is happening on a very old HTC Sensation running Android 4.0.3, and all the help found online refers to more modern versions.
Google Play Store, I forced stop, cleared data and cache, rebooted but it didn't cure the problem. I also performed a factory reset without success.
Someone in the Google Play Help Forum advised me to call the Play support team which I did. They sent me an email, I followed the procedure but it didn't fix anything. They told me to contact HTC if the bug still persisted, which I did a while ago but no reply, so far.