Depends. Both Denmark and Canada have long-standing claims to Hans Island, in the Nares Strait, between Ellesmere Island (Canada) and Greenland.
If the Danish claim is considered valid, and the Canadian claim is not, then Denmark is the closest European nation, since Hans Island is about 20 km from the coast of Ellesmere Island. If the Canadian claim to Hans Island is considered valid, and the Danish claim is not, then the issue becomes more complex. The reason is that, as of June 21, 2009, Greenland will be an independent country under the Kingdom of Denmark. That leaves sovereignty open to interpretation. If Greenland is considered under Danish sovereignty, as for example Wales is under the United Kingdom, then Denmark is still the closest European nation to Canada, through Greenland's proximity to Hans Island (again, about 20 km). If Greenland is considered as independent of Denmark as Canada is from the United Kingdom, then Denmark is not the closest European nation to Canada -- France is, through the islands of St. Pierre and Miquelon, about 25 km from the coast of Newfoundland.
Denmark and Canada agreed to demarcate their maritime boundaries in 1973 using 127 surveyed points between the Davis Strait (south) and the Robeson Channel (north). Hans Island is bisected by an imaginary line drawn directly between survey points 122 and 123. If both Denmarks' and Canada's claims to Hans Island are considered valid, and these nations using the maritime boundary as a basis for dividing Hans Island, Denmark will border Canada. It is also possible that both nations may someday agree on joint rule, perhaps making the two nations overlap at Hans Island. However, no resolution to the dispute has been reached yet.
I would think that it would have to be the UK, England: the United Kingdom of Great Britain and Northern Ireland. Same language, same basis in laws, similarity in culture, our "Mother England". Then possible the Republic of Ireland.
Well, no country is closet to it. It's a continent and there are many countries in it. Several countries and continents are touching Europe, so this is really an unanswerable question.
Ireland, then the United Kingdom, which is a very close neighbor
It's France. thanks to the islands of Saint-Pierre-et-Miquelon (19km from the canadian coast).
Portugal
Spain.
England shares borders with Scotland and Wales, so they are the equally closest European countries to England. The closest mainland European country to England, which may be what you mean, is France.
New Zealand is closest in size to Colorado.
Mexico is the closest country south of the US, as it borders the US to the south.
The closest European country to the North Pole is Norway.
EGYPT
US
New Caledonia is currently classed as a special part of France, (though that status is under review) and thus must be considered the closest part of a European country.
The closest European country to Africa is Spain.
Denmark is the closest mainland country to Greenland. There are 2,920 miles between the two countries. The second closest country is the Netherlands.
Ireland
Azores Island (Portugal)