Hello Julien,
Seems like that the location of your jobs are not being geocoded. In order for a location to be displayed on the map it must be geocoded and have coordinates in database. When location is properly geocoded you should see custom fields like geolocation_city, geolocation_state, geolocation_street, geolocation_lat and so on, in the Edit Job page.
When locations are not being geocoded it could be either the WP Job Manager geocoder that is disabled or that your website is getting OVER_QUERY_LIMIT error. It might also be a missing Google Maps API key.
First thing I would try is to install the WP Job Manager Client-Side Geocoder plugin. Client-side geocoder most time overcome the OVER_QUERY_LIMIT issue. After installing the plugin, you will see a new “Geocode Address” button below the address field of the “Edit Job” page. You need to click this button in order to geocode the address then update the job again to save the changes. Then, after the page reload, look for the geolocation custom fields mentioned above.
Let me know if that helps.