Hi Jessica,
You can add the password to the site in your next reply, and mark it as private.
I have checked the the ‘profilcooperateur’ custom post type on the back-end editor, but unfortunately there is no post content field there. Everything is generated via ACF fields, and the post content is empty, that is why the result content is empty. I guess the theme uses a custom template file in order to display these custom structured fields.
You could try using the advanced description field to try to display these field contents.
To make it easier for you, I have made a duplicate of the first search instance (search ID=5), and tried to get the ACF field names, and added them to the advanced content field, and configured it like so: https://i.imgur.com/rz8zS2Y.png
Now, in the preview, the results look like this: https://i.imgur.com/hAqMDGx.png
I believe this is very close to what you might need. In the advanced description field I added the following text and HTML, in case you want to make changes to it:
[<img width=240 src='{image-profil}'>]
[<br><h3>{prenom_nom}</h3>]
[<br><h3>{_taxonomy_atelier}</h3>]
[<br><h3>{_taxonomy_batiment}</h3>]
[<p>{_taxonomy_categoriesprofilcooperateur}</p>]
[<br><p>{adresse-atelier}</p>]
[<p>{adresse_email_du_cooperateur}</p>]
[<br><p>{presentation-cooperateur}</p>]
[<br><img width=320 src='{image-presentation-coop}'>]
{descriptionfield}Hopefully this helps a bit.