Hi and thanks for using our plugin. Your blog looks awesome. I always swim away from Jellyfish in the ocean but reading your article gives me a new perspective.
Our plugin translates the Permalink page name which helps for SEO. And you can edit the translated Permalink name using the GTS translation editor if you chose to post-edit your website content. But the part you want to remove (language/fr) is currently hard-coded into the plugin code and can't be changed. In your case, since you set up virtual hosts per language, it is indeed a useless and annoying addition to the URL. But most of our users do not set up virtual hosts.
I'll ask our developers if we can change this feature for users that implement the virtual host feature. But I am not sure how soon it will be done.
Please stay tuned for future upgrades to the GTS Translation plugin. In the meantime, I hope you are getting good benefit from our plugin and thanks again. Dave