You can have a look in this drupal documentation. In general you need to create a view that overrides the search result. In home website we have set the Preview List pattern in the used display and set the view to be rendered using the Teaser List display format.
Can’t I just modifiy this view (https://test-voisins2.web.cern.ch/search), or would it be possible to share with me a screenshot of the home.cern view so that I can copy it? I am not sure I am capable to create it from scratch.
This view is a default one. We can remove that only by creating CSS file where you can put display: none; to every element you don’t want to see. You’d have to install CERN override theme and delete field there.
For example in the screenshot you can see display: none; in the element for the first search result.