Every set of blanks can be filled in to make a country in exactly two ways:
BELARUS/BELGIUM crosses JORDAN/NORWAY
MEXICO/MONACO crosses CANADA/PANAMA
ALBANIA/ARMENIA crosses ROMANIA/SOMALIA
ALGERIA/AUSTRIA crosses FRANCE/GREECE
The geodesic between the capitals of Belarus and Belgium crosses the geodesic between the capitals of Jordan and Norway, intersecting in Poland. Similarly, other sets cross in the United States, Turkey, and Italy.
You can see all the crossings drawn on this map.
Indexing into WARSAW, WASHINGTONDC, ANKARA, and ROME by the number indicated yields WINE.