Hi Nathalie,
The search widget located on the navigation is indeed dedicated to the products. It is managed by
WPC AJAX Search for WooCommerce plugin. To remove the products search, please deactivate this plugin.
In case you want a global search feature, you need to use a different search. Can you please go to Customize > Appearance > Navigation > Search and activate “Display Search Form”. This way, a new search feature will be added to the navigation and include all the content of your website.
In case you wanna extend your search feature, you might wanna tale a look at this plugin: relevanssi.com.
Hope this will help you.
Cheers,
PS: Your website looks great!