Better advice for the coin toss than not letting the same person choose and toss would be to not let the person tossing catch the coin in mid-air.
Also, have a disinterested third-party be the one to toss the coin.
England is generally considered more defensible than France in Diplomacy because even though there is one extra avenue to attack the English supply centres, all avenues of attack are by sea.
Regardless, you don't win Diplomacy by sitting back and defending your home supply centres.
If you are invited to enter a rock-paper-scissors tournament, politely decline.
Numberphile is awesome.