The problem is solved. Thank you for your help!
The problem was finally similar to this one: VMWare ESXi 4.1.0 Automation: Insufficient permissions in host operating system
In order to solve it I added the "Acquire Guest Control Ticket" grant to the vSphere user which is linked to my VDP appliance. Whatever the user you are logged with in vSphere, only the user which is linked to your appliance matters. To make sure which one is it, you should have a look to the appliance's configuration client "https://your_VDP_appliance_IP:8543/vdp-configure/".
Note for french users: the grant is "Gestion par l'API VIX du système d'exploitation invité".
Kind Regards,
McPicsou
EDIT : if you face any problem logging in the flr client, you should have a look to these logs: \Logs\usr\local\avamarclient\bin\logs\VmwareFlrWs.log