If you can make a screencast/video showing exactly what you’re doing then we can point out where you’re going wrong. You need to make sure you’re selecting the correct menu from the drop down to edit, changing the labels in each of the menus that display on your site – both mobile and main menu – and then saving.
Loco-translate allows you extract the strings for the theme, you have to manually go in and provide the french words for the plugin to translate. The full userguide to loco translate can be found here – https://localise.biz/help/wordpress/translate-plugin/beginners#setup. Lot’s of people have translated this theme using this exact process so it definitely works.