KVM VM storage on external HDD fails with permission error

I would like to test KVM with OpenSUSE Tumbleweed.
I successfully installed KVM, but I am stuck creating my first VM.

The trick is that I want to have the VM's directory on an external HDD.

When I set the directory for the VM file, I get this error message:

Impossible de terminer l'installation : « Cannot access storage file
'/run/media/lowley/424b7b47-883d-42ac-b6f3-994c0c01c01f/sauvegardes/fedora-haskell.qcow2'
(as uid:471, gid:10): Permission denied »

I am not very strong at managing user rights. I set root to be a member of the kvm group, but I still get this error.

I launch it by entering virt-manager as myself, not as root (in fact, I have a shortcut on the desktop).

Can you help me?