Hi Stephane!
The results page layout is a theme feature, search plugins can’t change that. Most themes however have wide support for customizing the layout and fields displayed via theme editor features (such as Divi or Avada). The best and easiest way therefore to check the theme builders integrated with your theme, 99% of the time it’s possible.
Another possibility is to use a full featured page editor, such as Elementor. With page editors can replace the whole results page with their own loops that you can customize.
The 3rd possibility is to edit the theme files via a child theme. This I only recommend when none of the options above are available or possible. In your case it shouldn’t be too difficult actually. If I understand correctly you want to only replace the excerpt with an ACF text field of some sort?
If your theme doesn’t support customizations and page building is not available, I can take a look if you want to. For that however I will need temporary sFTP and back-end access as some file edits will be required for sure. Also, don’t forget the field name, I need that too in order to fetch it programmatically 🙂