Bordeaux

Red Bordeaux - Merlot and Cabernet Sauvignon, Cabernet Franc. 

Left Bank - Dominated by Cabernet Sauvignon

Primary Appellations are Medoc and Pessac-Leognan

Right Bank - Primarily relies on Merlot

St Emilion - Merlot, Cabernet Franc (Small quantities of Cabernet Sauvignon and Malbec) 

Pomerol -  Merlot, often with Cabernet Franc and smaller quantities of Cabernet Sauvignon

White Bordeaux - Sauvignon Blanc, Semillon, Muscadell

Burgundy

Red - Pinot Noir and Gamay

White - Chardonnay

In Beaujolais, the only grape permitted by law is Gamay  while Pinot Noir dominates in other regions   

Chablis village is where Chardonnay is the only grape allowed.

Meursault also grows Chardonnay

Rhone - North:

Red -- Dominated by Syrah (produces 5% of Rhone wines) which is generally the grape used, although Viognier is allowed. 

White -- Include Viognier, Roussanne and Marsanne. 

Rhone - South:

Grenache based with Syrah, Mourvedre and Cinsault (95% of Rhone wines)

Hermitage

Made from the Syrah grape. It’s the most famous wine from the Rhone Valley.