French Bouquet on VirginMedia
Just subscribed to French Bouquet via the WorldBox app on VirginMedia channel 834. It provides France 2, 3, 5 and a cartoon channel for £6.99 a month. It also carries BFMTV whose news broadcast is onscreen as I write.
Not sure yet how it works for recordings if at all as it is a streaming service but will check that out. You can cancel subscription after 30 days but as the upcoming shows look great I think I'll keep using.
Update Feb 2019
VirginMedia recently removed the WorldBox app so French Bouquet is no longer available on its platform. That's a pity because TV5MONDE has also withdrawn its content from both Virgin and Sky. It's still available to stream free of charge and programmes are available through catchup.