The hostname for the site in Local needs to be different than your live production site. If you create the Local site with the same hostname, then a hosts file entry is created that points that hostname to your computer, as opposed to the production site. This would cause you to then not be able to reach your production site from your computer.
When you create the Local site, make sure that the “Local site domain” field is set to something like “formationdz.local”. You will need to ensure that the imported site uses that hostname – that’s handled differently, based on how you’re performing the import.