Hi Enzo,
The fact that the menu shows correctly in one page and not in other pages shows that the problem is indeed the cache. I see that you have many layers of cache and you also have the SG Cache.
I went to X > Settings and clicked the clear style cache button and then cleared the SG cache but the problem is still there. Then I checked the front end of the page which has the problem and use the Google Chrome browser developer toolbar network panel which shows that the x-cache is enabled:

This means that the requests to your server are not handled by the web server you host your website in and you use a CDN to handle the page. If you use the Cloudflare you need to follow the steps below:
https://xthemetips.com/using-cloudflare-rocket-loader-with-x-pro-and-x5/928/
If you still have a problem please disable the Cloudflare completely and let the original server handle DNS and not the CloudFlare and test the case.
Finally, I suggest that you contact your hosting service provider and ask them to help you fix the cache problem.
Thank you for your understanding.