This video is in French but it is very clearly explained. My school-boy French suggests that the idea is to knock the bottom of the bottle gently to encourage the cork to ease out…
A beautiful Cape West Coast day, a romantic picnic on the beach and no corkscrew; et voilà, a perfect rock!.
The presenter first shows the bottle being knocked with the heel of the shoe but that creates too sharp a shock wave. So the idea is to reduce the shock wave. Put the fat end of the bottle inside your shoe against the soft inner sole and then tap the heel of the shoe firmly against the wall. This will ease the cork out gently. Rule number one, ease the cork out with a series of firm taps not one almighty whack.
(Vive le winklepickers !)
I guess this would work on a picnic provided there is a hard vertical surface, maybe a tree.