From experience, I know that the Raspberry Pi is powerful enough to do this, however, keep in mind that the upload speed on the side providing the stream must be high enough.
If on your side (France) you only have a basic ADSL connection (e.g. from Orange), the upload speed may not be high enough to provide a usable video stream: audio will be fine, but video will be really low quality in that case (again, from experience !)
To enhance the answer, as I may have misinterpreted your use case: in my case the VPN servers are installed at the 'sites' where the TV channels are available for normal home use (i.e. watching on a regular TV set), but additionally are available for watching on a pc or tablet.
In your case, you (in France) would be running the VPN server (on a Raspberry Pi), allowing your dad (in the US) to virtually connect (using VPN client software) to your local network and watch TV (using your subscription) on his pc or tablet (or even stream it to a TV set, e.g. using ChromeCast like devices)