Hi all again, Update on my strange situation : immediately after installing Solus, I updated the system.
After rebooting as recommended, I did not have any network !
So, I decided to reinstall Solus from scratch.
The 2nd time was a redo of the 1st one.
Therefore, I gave up with Solus.
This is too bad because when I tried it, everything seemed promissing.
Therefore, unless somebody has the solution of this weird issue, I will not go further with Solus.
Disappointed !
Thank you for your kind assistance.
Cheers to the Community :.

For help on an issue like this you need to share what flavour of Solus you are running and also a part number and manufacturer of your WiFi adaptor as an absolute minimum. Some error logs might help. This is not Windows, these guys do not know what is going on with your PC because there is no magic telemetry spying on you.
Solus has recently made a number of updates on the system kernel which provides the drivers for most of the hardware, if you have old hardware it might be that it is simply not supported on the latest kernel. If this is the case you might find a fix by installing the LTS version of Solus.
Alternatively try a USB WiFi adaptor that is a make and model known to work well with Linux.
Thanks.

Hi BuzzPCSOS, Thank you for your reply and sorry for my late answer. I think the problem comes from my old laptop, almost 9 years old. So, I am going to follow your advice and install the LTS version to avoid any issue. Thank you again for your concern and accurate answer. Best regards, Tman