Hey François! How are you doing?
First I should note some things for you, as recommendations… I don’t know about your server configurations but you’re most likely reproducing them in Local, so here it goes…
- PHP 7.0 met its EOL (End of life) Jan 2019, so it’s not recommended to use it, using PHP 7.1 is a good option for compatibility (with hosts) and security updates.
About it: http://php.net/supported-versions.php - This is more “personal” but the same goes for MySQL 5.5, it is old, somewhat insecure and slow, compared to 5.6 and 5.7 versions. I would recommend using 5.6 and preparing to migrate to 5.7 (I’m doing this right now)
About it: https://forums.mysql.com/read.php?20,660008,660016#msg-660016
Now, to the issue at hand, can you upload your log file from Local? If you need help with it: How do I retrieve Local's log file?
Also, do you have the WP_DEBUG option enabled? If not, you can add the code below (locally, not live) at the end of the wp-config.php
file:
define( 'WP_DEBUG', true );
This will make Wordpress display any errors it catches, so you can have a better idea of what’s happening.
One more question, what page are you accessing when you see this? Are you able to access /wp-admin and login?