If a mere bishop is a chateauneuf, doesn't give much room for the stronger pieces.
Only a Yank would consider serving all the wines in identical glasses!
Perhaps:
Black pawns: French table wine (plentiful, with a lust to expand!)
Black Rooks could be Chianti or a Rioja
Black knights: A California Cab
Black Bishops: Tuscan (price range would determine what sort!)
Black Queen: Margaux (of course!)
Black King: doesn't matter since it's never taken. In which case, a port, which looks and smells better than it tastes anyway.
White:
Pawns: Cavit Pinot Grigio
Rooks: Riesling
Knights: Chardonnay (California for blitz chess, Burgundy for serious games)
Bishops: (Ideally French) Chenin Blanc
Queen: Champagne
King: Well, the king of white wines is the Chablis. for people with more sense than money, perhaps a muscat d'oro, or a nice Yalumba tawny port?
Truth in advertising: I too am American.
(I know, it's a beer smiley. But the sentiment's right!)