hello!
the shop should work fine even if the templates are outdated. your problem is probably unrelated to this (i've been working on shop things the last 4 weeks with these outdated templates and the shop works for me).
i'd need to take a look at your website @peignauxmelodie to see why a product wont show.
seems like you dont even have woocommerce activated on your website
can you send your website address, /wp-admin/ username and password and a link to this topic to info@laytheme.com?
i will take a closer look