Well I managed to get down a rabbit hole, but as we're talking about European countries, the definitive list of "BIG" countries should be:
Big Country:
Germany (14, 3)
Spain (12, 4)
Russia (12, 1)
Italy (11, 2)
France (11, 2)
Netherlands (11, 1)
Czech Republic (11, 1)
England (11, 0)
Bubbling under (Little Feat?):
Denmark (10,1)
Portugal (9,1)
Recency bias (reasonable number of appearances but weighted towards more recent editions
):
Croatia (7,0)
Belgium (7,0)
Sweden (7,0)
Switzerland (6,0)
Turkey (6,0)
Plucky minnows:
Scotland (4, 0)
Wales (2, 0)
N. Ireland (1,0)
Ireland (3, 0)
Won but forgotten:
Greece (4,1)
My basis for this is appearances in
Euros finals (rather than World Cup, mainly because that's just what I looked at first) and
wins in the tournament.
Now it was a bit weird, because it was four teams only from its start in '60 until expanded to 8 in '84, 16 in '96 and 24 in 2016. But given the proliferation of actual countries since '95 that's also unsurprising. UEFA now has 55 member organisations (remember, no less than FOUR of these are from UK

). Croatia, for instance has missed only a single tournament since their first in '96, while three of the Czech Republic's appearances (and their win) cames as Czechoslovakia (though they still have five more appearances than their neighbours)
UEFA Members:
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