The home page won’t be seen in your FTP program because it isn’t just a file. Like WordPress, pages are presented as needed via templates and the database.
No matter how you approach it, for a multi-language site you’re going to have to completely re-do the text on each page that contains text, you won’t have a page for English and another page with the same content but in French. Both languages will need to be on the same page.
I don’t know that it is possible. If they were initially published with Lightroom, that publisher instance is tied to the old site. You might try changing the API url in Lightroom to see if it all reconnects. Maybe that will update the database in the new site so that the gallery page and descendant menus work as they need to.
I created from scratch the BIO page of the site I am redesigning to use the language selector.
I copied all the settings from the original lucnadeau.ca bio page into the new BIO page.
I uploaded the correct images for the background.
The language selector works on the navigation menus.
I corrected the menu in order for it to lead to the page.
And yet…consider these pages: https://lucnadeau.ca/fr/bio/ the French version of the bio page; https://lucnadeau.ca/en/Bio/ the English version;
and the new BIO page in https://pideja.ca/lucnadeau/bio/