Hi Romain Lacour,

Please make sure you logged in as system administrator while installing the app.

Please follow the below steps.
1.Create trailhead playground.
2. Get the credentials using below link.

https://force.desk.com/customer/portal/articles/2659738-how-to-get-a-password-for-my-trailhead-playground?b_id=13478


3)Get into https://appexchange.salesforce.com

4)In the top right corner in search dialogue box enter Data Assessment and click on the app
 
5)In the next page you get an option of Get It Now when you click on this button you will be prompted with two options

6)  a)Install in production
     b)Install in Sandbox
  choose the first option(Install in Production)

7)"This app does not list support for your edition of Salesforce. You can continue installation, but it may fail later in the process.", The above error will be displayed on the next page.Click on I accept terms and conditions and click on confirm and install button on the above page.

8)Now you will be prompted to log in with your developer edition login credentials(provide your trailhead playground credentials).

9)In the next step, you will be prompted with three options

   a)Install for Admins Only
   b)Install for All Users
   c)Install for Specific Profiles
  
  Choose the first option from the above(Install for Admins Only) then         click on install

10)Select on grant access and click on continue and click on done

11)Now connect to trailhead paly ground and refresh the page, on the top right corner in the app menu you will be able to see data assessment app.

Hope this helps you!

If this helps you, please mark it as solved so that it will be available for others as a proper solution.

Thanks and Regards
Sandhya