Maintenance/Coming Soon Mode

Review info in this thread and see if it works for you: https://wordpress.stackexchange.com/questions/75806/custom-maintenance-page

@t-p Thanks for your answer. Unfortunately I tried but no success…

there are plugins for that: https://www.ads-software.com/plugins/search/coming+soon

Correct, but most of these plugins are made to be used with WP themes only, they do not work with custom themes. I’m stil trying to find one that could work…

Perhaps you should ask the developer of your custom theme, because there’s really no reason why those plugins should not work with a well-built theme.

I’m the developper of the custom theme, it’s really a “regular” HTML, CSS, JS, PHP website,

I’ve tried for instance the : WP Maintenance Mode plugin, doesn’t work at all.

Is there anything that I should consider on my side ?

No idea. You might ask the dev of that plugin in their support area here what its requirements are.